The Gong Show
The preview show by the 40 poster presenters

#1

YKIS-2016

Instantons and Entanglement Entropy
Arpan Bhattacharyya and Ling-Yan Hung
Department of Physics and Center for Field Theory and Particle Physics,
Fudan University

based on work with Charles -Melby Thomson and P.C.H Lau, Arxiv:- 1606.xxxxx

Decay of False Vacuum andEntanglement Entropy
Entanglement Entropy

How robust is the area Law?

How easy (hard) to get volume law for local field theories ???
crucial to obtain correct ground state
Instanton tunnelingClassic example is Mexican Hat potential in

Dilute gas assumption and replica trick give us,

SEE = S0 + A(R)KP1 [(1logPn )0 |n=1log( i⇡e S0 )]This is the Instanton correction to the entropy , do an analytic continuation in time,
decay rate K enters into the entropy expression

Decay of False Vacuum in spin Chain
and Growth of Entanglement Entropy
Transverse Ising Model:

H=

J

X

z z
x
+
h⌃
i i +b
i i+1

i

X

z
i

i

Study the time evolution of the wave function which appears
like false vacuum| (t) >= eiHT |0 >|0 > +1 eigenstate ofz

We find the growth of entropy is bounded by the area law
Satisfy Lieb-Robinson BoundGauge Theory
Generic gauge groups the background pure gauge configuration can
be classified by different topological sectors.
These backgrounds cannot be related by small gauge transformation.
True vacuum is the sum of all these.
Vacuum.

✓Instanton tunnels between these pure Gauge backgrounds✓

Vacuum in 2+1d U(1) Gauge theory S =2+1 d U(1)Z

1 µ⌫d x 2 F Fµ⌫4e
3

X-Y model duality

X

Y

Z

Zn (N ), Zn (N ) =⇠in d2 x exp( SnN ),Give us handle how to do the n=1 Zn =
i
N =2m
Z
expansion and the answer for EE
XN
2
Sn / d x
qi qj Gn (xi , xj )matches from both side.
i,jModelling ✓ -Vacuum
One more classic example is 1+1 dimensional Schwinger model:
Sschwinger =✓Z

d x ¯ µ (i@µ2e Aµ )

Vacuum (in temporal Gauge) :

|✓ >=

X

exp

iN ✓

f0 (N, )

Y

exp

†
†
tn (j̃+n
j̃+n
j̃

n>0

N

j̃n,± = cosh n jn,± + sinh
Bogoliubov transformation

1 µ⌫
F Fµ⌫
4

n j̃

n)

|N >

†
¯ ±
n jn,± , j± =Too complicated , we will consider a toy model where we justfocus on the (weighted) sum of the Fermi-surfaces.
|

>=

L
X

N =1

N
Y
f (N, )
c†ki |0 >kiY
1 Xiki xjc k1 = pcj e, cj = (
L j
i<j

+
z
i) j

Entanglement entropy for this case cannot scale as “Volume”.

#2

Entanglement Entropy and Conformal Interfaces
Enrico Brehm, Ilka Brunner, Daniel Jaud, Cornelius Schmidt-Colinet
Arnold Sommerfeld Center, Ludwig Maximilian Universität München

June 15th 2016

CFT1

CFT2

correlations
E. Brehm

Entanglement Entropy and Conformal Interfaces

Measure of choice: Entanglement Entropy
SA = −Tr ρA log ρA = −∂Trρn .
∂n A

Method:
CFT⊗n
JI nbntop. defect bn

I ⊗n

B

A

Result:SI = σIclog L + s(I) .
3

E. Brehm

Entanglement Entropy and Conformal Interfaces

#3

Equivalence of Emergent de Sitter Spaces
from Conformal Field Theory
Claire Zukowski

C. T. Asplund, N. Callebaut, CZ [1604.02687]

Two proposals for a dS space emergent from entanglement entropy:
1) Kinematic Space
KS = Space of boundaryintervals in/spacelike
Ryu-Takayanagi geodesics ona bulk slice of2) Auxiliary de Sitter Proposal
Modular Hamiltonian for ball-shaped
regions forin vacuum:boundary-to-bulk
propagator
GlobalCzech, Lamprou, McCandlish, Sully (2015a)

satisﬁes a dS
Klein-Gordon equation
de Boer, Heller, Myers, Neiman (2015)

Our Results

Goal: Provide support for the equivalence of these emergent
spacetimes in the vacuum case and beyond

Pure AdSBTZ String

BTZ BH

Con. Sing.

Our Results:•Thermal Case: KS for BTZ black string is the hyperbolic patchof. Perturbations of EE satisfy a wave equation on KS.
•Quotient Spaces: For e.g. BTZ black hole/conical singularity,
phase transitions in EE introduce defects in KS.
•Causal Structure: KS of locally
hyperbolic.
Equivalence

spaces is generically globally

Modular Hamiltonian from EE?

Kinematic space K (1.0) = space of CFT2 intervals / AdS3 geodesics[Czech, Lamprou, McCandlish, Sully JHEP 1510 (2015) 175]
K of global AdS3
= global dS2

K of
Poincare AdS

K of
BTZ black string

K = auxiliary de Sitter of[de Boer, Heller, Myers, Neiman
Phys.Rev.Lett. 116 (2016) no.6, 061602]=>
EE perturbations propagate on K

K of
BTZ black hole

K ofconical star

K of quotiented geometries
raises questions on
propagating fields on K
[Asplund, NC, Zukowski
1604.02687]

Kinematic space K (1.0) = space of CFT2 intervals / AdS3 geodesics[Czech, Lamprou, McCandlish, Sully JHEP 1510 (2015) 175]
K of global AdS3
= global dS2

K of
Poincare AdS

K of
BTZ black string

K = auxiliary de Sitter of[de Boer, Heller, Myers, Neiman
Phys.Rev.Lett. 116 (2016) no.6, 061602]=>
EE perturbations propagate on K

K = auxiliary dS for any
locally AdS3 geometry, byrecognizing K as Liouvillemetric with the EE the
Liouville field[NC, Verlinde - in preparation]

#4

Emergent Geometry from RedundancyConstrained States and Bulk Entanglement
Gravity

ChunJun Cao and Sean Carroll,
California Institute of Technology
Prepared for YKIS 2016

Embedding
manifold

Entanglement
perturbation and gravity

#5

Entanglement Entropy in a Holographic Kondo Model
Mario Flory
Max-Planck-Institut für Physik

Quantum Matter, Spacetime and Information
YITP, 15.06.2016
Based on 1410.7811 and 1511.03666
Mario Flory

YKIS 2016

1/2

Entanglement entropy in the Kondo effect
3
0.065

T/Tc
1

0.060

1.5

2.0

0.055
0.050
0.045
condenses, Kondo cloud forms

0.040
0

Mario Flory

1

2

YKIS 2016

3

4

ℓ/zH

2/2

0

#6

 Bose-Hubbard model as the effective theory on an optical lattice, including

the hopping term + Short-range repulsive interactions U
 The extension to the SU(N) Bose-Hubbard model

Conjecture of MF-Harrison-Karch-Meyer-Paquette, JHEP04(2015)068

H   w (bai baj  baj bai )†SU(N) Bose-

Hubbard model

2d gravity on the
AdS2 hard wall† ij   nj jU
n j ( n j  1), ni  bai† bai
2 j To compute the VEV of the hopping term in both sides of the duality
concretely and compare them,Work in progress of MF-Meyer-Sumiran-Tezuka
YKIS 2016, Quantum Matter, Spacetime and Information

2016/06/15

1

(a)

(b)

 (b): Realizing the lobe-shaped phase structure from the gravity dual
 Finding zero modes at the cusp around thop=0(c) (c): Comparision of dF/dthop : the result of SU(Nc) Bose-Hubbard model fits the result of the gravity

dual at small hopping well (Dashed lines are the field theory result)

YKIS 2016, Quantum Matter, Spacetime and Information

2016/06/15

2

#7

Fractional quantum Hall states of dipolar fermionsin a strained optical lattice
Hiroyuki Fujita, ISSP. Univ. Tokyo

Aim:

Quantum simulation of strongly entangled phase of matter

Landau levels
Correlation

Synthetic magnetic field
in a strained honeycomb optical lattice

Fermionic dipolar molecule e.g. NaRb

Realization of FQHE states in ultra-cold gases?

Method:

Exact diag. in a spherical geometry in lowest LL

Result:Various valley-polarized FQHE states found

Norb

1
Energy scale estimation for ⌫ =3

Laughlin state ofDiscussion on its experimental realization

#8

Shape Dependence of Holographic
Rényi entropies.

Damián A. Galante (UWO/PI)
Work in progress in collaboration with L. Bianchi,
S. Chapman, X. Dong, M. Meineri and R. Myers

Lots of conjectures have been made recently about
universal features of Rényi entropies of deformed
entangling surfaces…
For 4d CFTs

fb (n) = fc (n)Cone Contributions to
Rényi Entropies

(d)
n /

hn
n

1

Displacement
conjecture in generaldimensions
CD (n) = d

✓

d+1
2

◆✓

2
p
⇡

◆d 1

hn

There has been a proof around n=1 [Faulkner, Leigh,Parrikar], but for general n…

Shape Dependence of Holographic
Rényi entropies.

Damián A. Galante (UWO/PI)
Work in progress in collaboration with L. Bianchi,
S. Chapman, X. Dong, M. Meineri and R. MyersIn 4d holographic CFTs
fb (b) 6= fc (n)In
In holographic
holographic CFTs
CFTs
in
in d
d dimensions
dimensions[X. Dong, 2016]

What is CD? How to compute it in holographic theories?
What is the result? How different is it from the conjecture?

#9

Dyonic extremal Black hole entropy for N = 8 gauged supergravity
Prieslei Goulart - IFT/UNESP - Sao Paulo, Brazil - MPI - Munich, Germany
I

Motivation: obtain the black hole entropy for supergravity theories with a
non-trivial dilaton potential;

I

Sen’s entropy function:
Near horizon metric is AdS2 × S 2 :
dr 2
ds 2 = v1 −r 2 dt 2 + 2+ v2 (dθ2 + sin2 θdφ2 ),r(1)

where the constants v1 and v2 are the AdS2 radius and the S 2 radius respectively.
Entropy function:Zp
E(~u , ~v , ~e , ~q , ~p ) ≡ 2π[eA q A − dθdφ − det g L].
(2)
Attractor equations:
∂E
∂E
∂E
∂E
= 0,
= 0,
= 0,
=0,
∂us
∂v1
∂v2
∂eA

(3)

At the extremum (3) the entropy function is the black hole entropy:
SBH = E(~u , ~v , ~e , ~q , ~p ).
Prieslei Goulart

(4)

I

We obtain the dyonic black hole entropy N = 8 gauged supergravity:




Z
4
4
X
X
X
1
3
2
µ
2
I
2
4 √
(∂µ λI ) − 2∂µ λI ∂ λJ  −X (F ) − V  ,S=
d x −g R − 
8 I =14 I =1 I µν
I <J
(5)
I
Fµν
= ∂µ AIν − ∂ν AIµ ,I

g2 X 1V (X ) = −, X1 X2 X3 X4 = 1.
4 I <J XI XJ(6)The entropy is written as

E = 2π4XI =1!
q I pI

v

u
u
1
g2
u
 
 1 + t1 −22−1/2!X r pJ pK q I pI 
.
qJ qK
I =1
J<K

4
X

(7)
I

The entropy can also be written as
1
E=
2

I

4
X

I

q pI

I =1

!

q1 q2 q3 q4
p1 p2 p3 p4

1/4.

We also how the entropy changes under electric-magnetic duality.

Prieslei Goulart

(8)

#10

String theory is not even wrong?
Not really; we will make it FALSIFIABLE!

PLANCK
LIGO

Today we propose yet another approach:an experimental realization of a quantum black holeSuper Yang-Mills

IIA/IIB-string
M-theory(BH, black brane)

Sachdev-Ye-Kitaev
model

BH in AdS2Make them fromatoms and lasers!

Experimental Quantum Gravity
with Cold Atoms
I. Danshita, M. Hanada, M. Tezuka©NIST

Let’s make a black hole in your lab and see how it behaves!

#11

Hayata, Hidaka, MH, Noumi, Phys. Rev. D 92, 065008
MH in preparation (2016)

Emergent curved spacetime
from locally thermalized matter
Described by
T (x), v(x), µ(x)QFT

Masaru Hongo
iTHES Research group, RIKEN
Quantum Matter, Spacetime and Information, 2016/6/15, Kyoto University,

Thermal Field Theory
Thermodynamics

Thermal Field Theory0

T = const.

dPath int.

( Matsubara, 1955 )QFT in theflat spacetime0with radius

0x
Gibbs distribution: ˆG =e

(Ĥ µN̂ )=e(Ĥ µN̂ )± |e(Ĥ µN̂ )[ , ]Z
Thermodynamic potential with Euclidean action[ , ] = log Tr e

(Ĥ µN̂ )= log( )=± (0)

= log

d

D e+SE [ ] , SE [ ] =d0|d3 x LE ( , µ )Local Thermal Field Theory
Local Thermal Field Theory

Hydro { (x), v(x)}[ Hayata-Hidaka-MH-Noumi ’15 ]QFT in thedPath int.

(x)x[t̄; ]

log Tr exp

d

t̄

µ

“curved spacetime”
with “metric”g̃µ = g̃µ ( , v)(x)T̂ µ (x) + (x)Jˆ (x)[ ] is written in terms of QFT in curved spacetime
2

ds =

2

ī

e (dt̃ + aī )dx +0īj̄īj̄ dx dx

Symmetry = Spatial diﬀeomorphism + Kaluza-Klein gauge
Consistent with [Banerjee et al.(2012), Jensen et al.(2012) …]

#12

Crofton’s formula
Czech etal. 2015σ(γ)
14G = 4 ∫γ∩Γ≠∅ N(γ ∩ Γ) K

G1Γ

The length σ(γ) of a curve γ can be
expressed in terms of an integral over thegeodesics Γ that have nonvanishingintersection number N(γ ∩ Γ) with γ

The measure K is given by the second derivative of theentanglement entropyK (u, v ) =∂ 2 S(u,v )∂u∂v du ∧ dv

Hence we can obtain the geometry from the entanglement
structure of the field theory on the boundary
Xing Huang

Some applications of integral geometry in AdS/CFT

Kinematic space of geodesics in general dimensions
XH and Lin 2015
Crofton’s formula in higher dimensions:Aσd (M d ) ∼ ∫M d−1 ∩Γ≠∅B

N(M d ∩ Γ) K

which says that the area is equal to flux ofgeodesics

K =1∂ 2 S(⃗
x1 , x⃗2 ) d−1 idet [] ∏ dx2 ∧ dx1i
4G
∂ x⃗1 ∂ x⃗2
i=1

Xing Huang

The volume form follows fromsecond derivative of S and is a new
type of measure of two-point
correlation (entanglement contour)
S is no longer related to entropy
even though it can be computedfrom field theory

Some applications of integral geometry in AdS/CFT

#13

Coupled Wire Construction
and generalized Wilson line

YKIS2016

Yukihisa Imamura and Keisuke Totsuka (arXiv:1605.09235)
Coupled Wire Construction :A new method of systematically constructing topological phases
many-body hopping interaction(Abelian)
Laughlin statechiral spin liquid(Non-Abelian)
Moore-Read state
Read-Rezayi stateetc.
CFT (Luttinger liquid)Coupled Wire Construction
and generalized Wilson line

YKIS2016

Yukihisa Imamura and Keisuke Totsuka (arXiv:1605.09235)

The bulk theory of the Laughlin state= the Chern-Simons gauge theory
How emerging in the coupled wire construction?

The ground state has some redundancy
related to a gauge and a chiral transformation

generalized Wilson line :Chern-Simons gauge ﬁeld

#14

Topological phase transition in QCD
described by using imaginary chemical potential
K.K. and A. Ohnishi, PLB 750 (2015) 282.
K.K. and A. Ohnishi, arXiv: 1602.06037, to be published in PRD.

We propose a new determination of the confinement-deconfinement transition in QCD
The Roberge-Weiss endpoint would define
the deconfinement temperature

Effective potential
Confined phase

Deconfined phase

In this determination,
the deconfinement transition
can be interpreted as
the topological phase transition
This determination may have direct relations with the entanglement entropy and the Uhlmann phase#15

Distinguishability of countably many states
Ryuitiro Kawakubo and Tatsuhiko Koike, Department of Physics, Keio University
Theme:
State discrimination (We want to distinguish each state in a given set of states).
Problem:What kind of states can be distinguishable by a single measurement?
More precisely, in our discussion distinguishability of states is to be understoodas the possibility of an unambiguous measurement on them.
• An unambiguous measurement is allowed to answer“?” or “do not know”.
• An unambiguous measurement distinguishes the
inputs with certainty unless “?” is detected.
✴ Condition for distinguishability
We obtained
countable pure states to be distinguishable.

1

1

2

2

3

3
?

unambiguous measurement

Distinguishability of countably many states
Ryuitiro Kawakubo and Tatsuhiko Koike, Department of Physics, Keio University✴ Distinguishability of von Neumann lattices
A von Neumann lattice is a family of states which corresponds to the lattice in the classicalphase space. The distinguishability of a von Neumann lattice depends only on the area of its
fundamental region S. It is indistinguishable when S is sufficiently small and distinguishable
when S is sufficiently large. The threshold is exactly the Planck constant,which is the unit of area of the phase space as in Bohr-Sommerfeld quantum condition.

indistinguishable

distinguishablehthe Planck constant

S

#16

#17

Holographic Entanglement Entropy of
Anisotropic
Minimal Surfaces in LLM Geometries
YKIS2016 Quantum Matter, Spacetime and Information
June 13-June 17, 2016 YITP, Kyoto University, Japan
In collaboration with Chanju Kim, O-Kab Kwon
Based on arXiv1605.00849 (accepted in PLB)
Previous related works
Phys.Rev. D90 (2014) 4, 046006 ,Phys.Rev. D90 (2014) 12, 126003(with O. Kwon, C. Park and H. Shin.)
Kyung Kiu Kim(Yonsei University) Vacuum structureContinuous Vacua

 Entanglement Entropy ?

Discrete Vacua

 An infinite number of entanglement entropies

 We consider all the entanglement entropies corresponding to

all the vacua through a holographic approach(Ryu-Takayanagi
Formula).
 For small mass deformation

 This result should correspond to the corresponding field

theory calculation with small mass perturbation.

 There are many interesting structures( Droplet picture, Yong

diagam, H c-theorem). Please visit my poster presentation !
Thank you !

#18

Dynamic correlation of Kitaev’s honey-comb model
Shinji Koshida
Department of Basic Science, The University of Tokyo

June 15, 2016
A
B
1

2

HKit = −∑µ=1,2,3Jµ∑Sxµ Syµ .

µ(x,y)∈BΛ3

1/2

• By mapping the Kitaev’s honey-comb model to Majorana fermions coupled toZ2 -gauge fields,

H̃ =

i ∑
Axy a4x a4y4x,y∈Λ

acting on an extended Hilbert space, it is “solved”.

• The action of quantum spin operators is not clear.
• I derived matrix elements of quantum spin operators with respect to energy

eigenstates.
′⟨ϕσI , S̃xµ ϕσ0 ⟩


∑
∑
′
′
′
′
σ
σσ
σ ′ PfZ σσ 
= C σσ (−1)ℓ(I,i) Rxi
PfZI∪{i}+(−1)ℓ(I,i) Rxi
I\{i}
i∈I\I

i∈I
2/2

#19

Time-evolution of Holographic Entanglement Entropy and Metricperturbations
Jung Hun Lee (Kyung Hee Univ.)
Based on (arXiv:1512.02816) with Nakwoo Kim (Kyung Hee Univ.)

Entanglement Entropy has holographic descriptions of quantum gravity
by AdS/CFT correspondence. [Ryu,Takayanagi 06]

von Neumann: SA =
formulaHolographic EE : SA =TrA [⇢A log ⇢A ]Area( A )4GN (d+1)

The motivation is to see how small excitations in the gravity side manifest
itself in HEE.
We consider the small cap-like surfaces in the bulk and compute HEE
perturbatively in deformed AdS vacuum. (ex. AdS-BHs, AdS-scalar systems)

Yukawa International Seminar 2016 (YKIS2016)
Quantum Matter,Spacetime and Information

Time-evolution of Holographic Entanglement Entropy and Metricperturbations
Jung Hun Lee (Kyung Hee Univ.)
Based on (arXiv:1512.02816) with Nakwoo Kim (Kyung Hee Univ.)

We found that the metric perturbation around the AdS vacuum does not effectthe divergent terms and the change is in the finite part.
We have computed the entanglement temperature by using the methods ofholographic renormalisation. [Bhattacpatya,Nozaki,Takayanagi,Ugajin 13][Fe↵erman,Graham 85][Myers 99]

We have checked that the entanglement temperature is proportional to theinverse size of the system and has the same value for the systems consideredin our paper.

Thank you for listening!

Yukawa International Seminar 2016 (YKIS2016)
Quantum Matter,Spacetime and Information

#20

ArXiv: 1603.01777

1. Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah, 84112, U.S.A.
2. Key State Laboratory of Surface Physics, Department of Physics and Center for Field Theory and Particle Physics, Fudan University, China
3. Collaborative Innovation Center of Advanced Microstructures, Fudan University, China

YITP, May 2016

Quantum Entanglement in Topological Phases on a Torus
1. Phases with intrinsic topological order have (among other features),1) ground state degeneracy on nontrivial manifolds;
2) bulk-edge correspondence;3) long-range entanglement.
2. What does entanglement for such phases look like on nontrivial manifolds?
How do these degenerate ground states enter?
What other information is involved?
3. These questions have been partially studied before[1] using Chern-Simons
theory. We focus on a general set of non-chiral theories: string-net model[2].
[1] Dong, Shiying, et al. Journal of High Energy Physics 2008.05 (2008): 016.
[2] Levin, Michael A., and Xiao-Gang Wen. Physical Review B 71.4 (2005): 045110.
YITP, May 2016

4. By partitioning a torus into two cylinders, we derive

5. A decomposition matrix M enters the expression which describes how bulk topological charges of theground states decompose into boundary degrees of freedom.

6. We generalize the Minimally Entangled States[3] to Minimally Entangled Sectors.
7. Examples from abelian & non-abelian finite groups and modular tensor category are discussed.
[3] Zhang, Yi, et al. Physical Review B 85.23 (2012): 235151.
YITP, May 2016

#21

Spectral Weight in
Holographic Superfluids
Victoria Martin
Stanford University
arXiv:xxxx.xxxx Gouteraux, VM
See also: arXiv:1210.1590 Anantua, Hartnoll, VM, Ramirez

Quantum Matter, Spacetime and Information
June 15, 2016

Charge behind horizon

Low energy spectral weightat nonzero momentum

𝜎≠0

𝑘 < 𝑘⋆

𝜎≠0𝑘 < 𝑘⋆

𝑘 < 𝑘෨

𝜎≠0

?

?

𝜎≠0

𝑘 < 𝑘⋆

𝑘 < 𝑘෨

𝜎≠0

?

?

1)

How should we interpret low energy spectral weight that exists independently of charge?

2)

What other degrees of freedom could this weight represent?

3)

To what extent do bulk charge distribution properties represent those of the boundary charge?

#22

Quantum Entanglement in the de Sitter Spacetime
Akira Matsumura
Yasusada Nambu (Nagoya univ.)

Hubble Horizon

Hubble Horizon
Inflation

A

Disentangle?
Entangle
We investigated the entanglement in the de Sitter space.

The entanglement
does not disappear .

In this scale, the entanglement is lost.

Discussion :What a relation between the entanglement and the de Sitter
spacetime structure ?

#23

Holographic Entanglement Entropy (HEE) and Field
Redefinition Invariance (FRI)
M. R. Mohammadi MozaﬀararXiv: 1603.05713

in collaboration with A. Mollabashi, M.M. Sheikh-Jabbari, M.H. Vahidinia
IPM (School of Physics)

June 2016

M. R. Mohammadi Mozaffar (IPM)

HEE and FRI

June 2016

1 / 3

Field Redefinition InvariancePhysical observables must be invariant under the field reparametrization(change of basis in the Hilbert space)
Example: Path Integral in QFT

Z=∫

DΦ(x) e−I[Φ(x)] =Φ(x) → Φ̃(x) = Φ̃[Φ(x)]∫DΦ̃(x) e−I[Φ̃(x)]˜

non-zero Jacobian

A one-to-one correspondence between physical observables
Question
Can we find HEE functional for higher derivative gravity theories using FRI?

M. R. Mohammadi Mozaffar (IPM)

HEE and FRI

June 2016

2 / 3

HEE and FRIOur Strategy∫√
gR + ...

Ryu-Takayanagi
Field Redef.

SEE = min(A)
4G

G(g)
∫√
gf (Rµν ) + ...

G −1 (g)FPS, Dong & ...

SEE

Achievements
FRI extracts the new HEE functionals from the RT functional, so
1

It gives both the HEE functional and the corresponding hypersurface2

It has simple generalization to time dependent cases

3

Diﬀerent entanglement inequalities satisfied

M. R. Mohammadi Mozaffar (IPM)

HEE and FRI

June 2016

3 / 3

#24

.
.

Field Space Entanglement: Scalar Fields
Ali Mollabashi
School of Physics
Institute for Research in Fundamental Sciences (IPM), Theran

Based on JHEP 03 (2016) 015 (arXiv: 1509.03829),
in collaboration with M.R. Mohammadi-Mozaffar

Ali Mollabashi

0 / 2

Field Space Entanglement
Consider a local QFT with N number of fields
L = L1 [ϕ1 (x)] + L2 [ϕ2 (x)] + ⋯ + LN [ϕN (x)] + Lint. [ϕi (x)]Ali Mollabashi

1 / 2

Field Space Entanglement
Consider a local QFT with N number of fields
L = L1 [ϕ1 (x)] + L2 [ϕ2 (x)] + ⋯ + LN [ϕN (x)] + Lint. [ϕi (x)]Hilbert space decomposition
Htot. = H1 ⊗ H2 ⊗ ⋯ ⊗ HN

Ali Mollabashi

1 / 2

Field Space Entanglement
Consider a local QFT with N number of fields
L = L1 [ϕ1 (x)] + L2 [ϕ2 (x)] + ⋯ + LN [ϕN (x)] + Lint. [ϕi (x)]Hilbert space decomposition
Htot. = H1 ⊗ H2 ⊗ ⋯ ⊗ HN
Reduced density matrix
ρ(m, N ) = TrH(N −m) [ρtot. ]Ali Mollabashi

1 / 2

Field Space Entanglement
Consider a local QFT with N number of fields
L = L1 [ϕ1 (x)] + L2 [ϕ2 (x)] + ⋯ + LN [ϕN (x)] + Lint. [ϕi (x)]Hilbert space decomposition
Htot. = H1 ⊗ H2 ⊗ ⋯ ⊗ HN
Reduced density matrix
ρ(m, N ) = TrH(N −m) [ρtot. ]Entanglement and Renyi entropies
Sent. = −Tr [ρ(m, N ) log ρ(m, N )]Ali Mollabashi,

S (n) =

1log Tr [ρn (m, N )]
1−n

1 / 2

Field Space Entanglement
Consider a local QFT with N number of fields
L = L1 [ϕ1 (x)] + L2 [ϕ2 (x)] + ⋯ + LN [ϕN (x)] + Lint. [ϕi (x)]Hilbert space decomposition
Htot. = H1 ⊗ H2 ⊗ ⋯ ⊗ HN
Reduced density matrix
ρ(m, N ) = TrH(N −m) [ρtot. ]Entanglement and Renyi entropies
Sent. = −Tr [ρ(m, N ) log ρ(m, N )],S (n) =

1log Tr [ρn (m, N )]1−nExplicit models
S=
Ali Mollabashi

N
1
2
d
µ
∫ d x [∑ (∂µ ϕi ) + λ ∑ ∂µ ϕi ∂ ϕj ]
2
i=1
1 / 2

Our (Gaussian) Models
Nearest-Neighbour

Infinite-Range

ϕ3
ϕ4

ϕ3
ϕ2

ϕ5

ϕ1

ϕ6

Ali Mollabashi

ϕ4

ϕN

ϕ2

ϕ5

ϕ1

ϕ6

ϕN

2 / 2

Our (Gaussian) Models
Nearest-Neighbour

Infinite-Range

ϕ3
ϕ4

ϕ3
ϕ2

ϕ5

ϕ4

ϕ1

ϕ6

ϕN

ϕ2

ϕ5

ϕ1

ϕ6

ϕN

Renyi & Araki-Lieb inequalities and SSA are satisfied
n-partite information ≥ 0 (checked for n ≤ 5)
In particular I (3) ≥ 0 (existence holographic dual?)
Infinite-Range model in λ → 0 limit
S reg. (m) =Ali Mollabashi

λ2 m(N − m)
λ2 m(N − m)
[1 − log] + O (λ3 )
32
32
2 / 2

#25

The Gibbs paradox revisited from theﬂuctuation theorem with absolute irreversibility
1University of Tokyo, 2RIKEN CEMS

The Gibbs paradox
from gas mixingYûto Murashita1, Masahito Ueda1,2

Sid = 0

Sdif = 2N kB ln 2

The Gibbs paradox has three faces
Gibbs (1875) GP-I
Thermodynamics

S

GP-II

S

Gibbs (1902)

GP-III Ehrenfest&Trkal (1921)
stat(Classical) statistical mechanics

The three faces are resolvedin the thermodynamic limit

van Kampen (1984)
Jaynes(1992)

However, GP-II is partially open in small systems!
YKIS Conference

15th June, 2016

The Gibbs paradox revisited from theﬂuctuation theorem with absolute irreversibility
1University of Tokyo, 2RIKEN CEMSYûto Murashita1, Masahito Ueda1,2

Theme of GP-II
S(T, V, N ) = S stat (T, V, N ) + kB f (N )Removing the ambiguity f (N )*The quantum resolution is irrelevant in this context

In the thermodynamic limit
N ln N + N const.

In a small thermodynamic system
Fluctuation theorem withabsolute irreversibility , f (N ) =
(W
F)
he
i=1
YKIS Conference'

Extensivity, f (N ) =S(T, qV, qN ) = qS(T, V, N )ln N ! (N ! 1)ln N ! + N const.
15th June, 2016

#26

Flux	
  quench	
  in	
  a	
  system	
  of	
  interac4ng	
  spinless	
  fermions	
  in	
  one	
  dimension	
  

Yuya	
  Nakagawa	
  (ISSP,	
  Univ.	
  of	  Tokyo)	

Nakagawa,	
  Misguich,	
  Oshikawa,	
  arXiv:1601.06167	

• Quantum	
  quench	
  of	
  the	
  ﬂux	
  piercing	
  an	
  interac4ng	
  spinless	
  fermion	
  chain	
  • Numerical	
  calcula4on	
  of	
  the	  dynamics	
  of	  par4cle	
  current	
  aHer	
  the	
  quench	
spinless	
  fermion	  chain	Flux	1†
H (t) = − ∑ ( e−iθ (t )ci†ci+1 + eiθ (t )ci+1
ci ) − Δ∑ ni ni+1ii
2

Dynamics	
  of	
  m
θ=omentum	
  π/3, ∆= -0.5 distribu4on	Dynamics	
  of	
  the	
  current	
  0.35

θ = π/2

0.3∆= -0.1
-0.3

J(t)

0.2
-0.5
0.5

0.15
0.1

0.1

nq

0.25

0.3

-0.8
0.8

0.05

-1.0

0

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

t=0
t=3
t=5
t=10
t=15
0.28
0.26
0.24
0.22
0.2
0.18
0.16
0.14
0

-1 -0.8 -0.6 -0.4 -0.2

-2.0 -1.2 -1.5

5

10

15
t

0

5 10 15 20 25 30

0.2 0.4 0.6 0.8
t1

Momentum q /π

-0.05
0

J(t)

20

25

30

4me	

Oscilla4ons	
  are	
  due	  to	
  selec4ve	
  Umklapp	  scaRering!!	
  Other	  results:	
  ・	
  strong	
  nonlinearity	
  of	
  J(t=∞)	
  in	
  rela4on	
  with	  the	
  Drude	
  weight	
  ・ thermaliza4ons	
  in	
  integrable	
  model	please	  see	
  .gif	  anima4on!	

Flux	
H (t) = −1†e−iθ (t )ci†ci+1 + eiθ (t )ci+1
ci ) − Δ∑ ni ni+1
∑
(
i
i
2

arXiv:1601.06167	

#27

Quantum Annealing with
Hyperpolarized Nuclear Spins
M. Negoro @ Eng. Sci., Osaka Univ.
Proposal for nuclear ferro or anti-ferro @ room temperature
0.5uK
Δω
0
ω1
0

Spin-Orbit Int.

Laser
microwave

0

t

34%
Laser
NuclearSpinmicrowave
Electron spin Orb.

Mom.

Spin-Orbit Int.

@100mK

#28

Entanglement dynamics of Majorana fermions
Takumi Ohta

Yukawa Institute for Theoretical Physics, Kyoto University

With Shu tanaka, Ippei Danshita, and Keisuke Totsuka
Reference: Phys. Rev. B 93, 165423 (2016)

Dynamical properties of Majorana fermions・Sweep dynamics with OBC
Sweep from C phase to C* phase: Sweep time・Physical quantities
String correlation functions (SCFs)
entanglement entropy (EE), spectrum (ES)Digest of Dynamics
Spatially periodic structure ＠ t = τ
SCF

EEOscillating and splitting structures in time
ES

#29

YKIS at YITP

Kyoto, Japan (June 2016)

Universality of Black Hole Quantum Computing
Benedikt RichterPhysics of Information and Quantum Technologies Group, IT, Lisboa
IST, Universidade de Lisboa
ASC, Ludwig-Maximilians-Universität München

joint work with

Gia Dvali

Cesar Gomez

Dieter Lüst

Yasser Omar

(LMU, MPP, NYU)

(LMU, UAM-CSIC)(LMU, MPP)

(IT, IST)

based on arXiv: 1605.01407

Black Hole Quantum Computing
By analyzing the key properties of black holes, we derive a model-independent
picture of black hole quantum computing.
Black hole type quantum computer

qubitsgates

decoherence time

Main results:
time scales for gate operations, (local) decoherence and life-time coincide:tgate ∼ tdecoh ∼ tlife−time⇒ maximal circuit depth is trivial,⇔ Trade-off between memory and information processing capacity

#30

“Quantum Matter, Spacetime and Information”,
June, 13-17, 2016

Paola Ruggiero

THE ENTANGLEMENT NEGATIVITY
IN RANDOM SPIN CHAINS
with V. Alba, P. Calabrese
arXiv:1605.00674

ENTANGLEMENT NEGATIVITY IN MANY BODY SYSTEMS

EA1 : A2 = ln T r|⇢T2 |“Good Measure” of Entanglement:

Pure states
Mixed states

QFT methods: [Calabrese, Cardy, Tonni, 2011]
Replica Approach:Exact results available in CFT:NEGATIVITY IN RANDOM
B2
B1 CHAINS
A1 SPIN
A2

B2

STRONG DISORDER RG
Random Singlet Phase(XX, Heisenberg, Ising)

B2

`1

r

A1

B1

`2

A2

B2

Single Realizationof the Disorder:

EA1 :A2 ⇠ nA1 :A2 log 2

Average over disorder (SDRG)
Adjacent intervals:
✓
◆
log 2
`1 `2
hEA1 :A2 i ⇠log
6`1 + `2

Disjoint intervals:
✓
◆
log 2
`1 `2
hEA1 :A2 i =log 1
6(`1 + r)(`2 + r)

#31

Entanglement Entropy of Scattering Particles
Shigenori Seki
This poster presentation is based on the work:
R. Peschanski (IPhT, CEA-Saclay) and SS,“Entanglement entropy of scattering particles”, Phys. Lett. B758 (2016) 89.

QUESTION
Let us consider a scattering process of two particles.
unentangled
initial stateA

B
interaction

final state(two particles)A|inii = |~k iA ⌦ |~k iB (center of mass)

S-matrix S

B|fini = QS|inii( Q : projection operator onto theHilbert space of two-particle states)

What is the entanglement entropy between the particles in the two-particle final state?

OUR ANSWER
There are elastic and inelastic channels: A + B ! A + B
A+B !X“elastic”“inelastic” (multi-particle)

By using partial wave expansions, we calculate the entanglement entropy;P` (2` + 1)s`ln P0
2`,`0 (2` + 1)(2` + 1)|s` |

SEE =

p~
A

~k

✓

p~

~k

2

B

X
⇡k
~
hh~
p |s|k ii =(2` + 1)s` P` (cos ✓)EA~k + EB~k`s` = 1 + 2i⌧` ,1Im⌧` = |⌧` |2 + f`2

(unitarity)

By introducing the physical Hilbert space, we obtain the formula that describes theentanglement entropy in terms of physical observables;

SEE =ln K ,

K⇠1

1 d elel
R2 dt t=0
4⇡R2
inel

el : integrated elastic cross sectiond el: differential elastic cross section
dt

inel : integrated inelastic cross section

R : maximal impact parameter#32

Z4 topological crystalline insulators and superconductors
Ken Shiozaki, University of Illinois at Urbana Champaign
KS, M. Sato, K. Gomi, arXiv:1511.01463• Topological insulators + nonsymmorphic space group• Periodic table from K-theory• Glide + Time-reversal symmetry → Z4 phase=

Z4=１ phase
Z4=2 phase

#33

Sudden Death and Birth of Topological Entanglementin 1D Fermions at Finite Temperature
YeJe Park, Seung-Sup Lee and Heung-Sun Sim*KAIST, Korea
Question

Our solution

At T = 0,
Use mixed-state entanglement measure 𝜀𝑋|𝑌 (𝜌)a topological phase defined in terms of GS.
to introduce a topological quantity 𝚪𝜺 (𝝆).
At T > 0,
how do we characterize a 1D topological SC ?
A
BC

Temperature𝚪𝜺 (𝝆) = 𝜀𝐵|𝐴𝐶 𝜌 − 𝜀𝐴|𝐵𝐶 𝜌 − 𝜀𝐶|𝐴𝐵 (𝜌)?
Topological

𝑻=𝟎
Trivial

QCP𝝁𝚪𝛆
Topological

Trivial𝝁SuddenDeathandandBirth
Birth of Topological
SuddenDeath
TopologicalEntanglement
Entanglement
1DFermionsFermions at
at Finite
Finite Temperature
inin1D
Temperature
YeJe Park, Seung-Sup Lee and Heung-Sun Sim*KAIST, Korea
Topological quantity Γ𝜀 at T > 0

Majorana fermions as entangled nonlocal qubits

Temperature𝚪𝜺In the topological region at T > 0,
the nonlocal qubits formed by bulk Majoranas
are entangled.
A

B

𝟏 𝟐

𝟑 𝟒

𝟐 𝟑 =

𝟏 𝟒 =

+

𝝁

C

#34

A few examples for Holography vs. experimentSang-Jin Sin (HYU)
2016.06.15@Kyoto

1

inal resistivity at H = 0 is

H
H resistivitys 0
The transverse
is given byion between ⇢xx and q30 Rs with µ/T = 0.1(black), 1(red), 2(blue), 5(green)where RH2 is1usual
and Rs is called anomalous Hall coefficient.
+⇠µ2Hall/⇢ 2 coefficientr02 6 q Since then log-log plot. q30 R
⇠
⇢
or
in
small
(
large
)
/µ
regime.
Arrowx = xx
xx
⇢H
=(23)
:=
⇢xx
.
↵
4
8 2
2
2 2
2
2
2 2

vityAnomalous
can be written
Hallascoeﬃcient Rs

asing

that
good ideaq to+checkr0 ( whether+µ ) o+ (1 +µ /Rs has) scaling behaviour ⇢xx , it isH=0
and we fixhasq been=✓1.known
non-linear result contains it asa special limits. Phys.Le6. B759 (2016) 104-109
arXiv:1512.08916

2
where
we use (15) in the
step.
ThenY.Seo
the anomalousHµ limit,⇠ Rwhile⇢⇠. Therefore
weis have
xx
⇢HRs⌘
H
+
R
The transverse
given by
KY.lastKim,
KK.Kim,
+(20)
sj
H
sM
0 ,resistivity
4model and background solution: With motivations described above, we
quasi particles. Therefore it is notThesurprising
to getthe same result3 with 1
2 6

the Einstein-Maxwell-axionraction
interaction
q with the Chern-Simons
Rs M
(24)
For Intrinsic deﬂecMon/ Rs ⇠ ⇢2xx .
s =
80
9
⇢H
=
:=
R
,
0
2Z+ (1 + µ2 / (2
2)
4
8 qR
2 +
2+
2 )are
2
Z
r
µ
✓
< and
=
0
In Sidelargejump/µ limit, or in the large theta
limit⇢
related
by
r
(
µ
H=0
X
s
xx
p
0
6
1 2
1
1
2
22 S = Hall
d4 x
g coefficient.
R+ 2
F(@ Since
qthere(@ I )2 F ^ F +I)
nt and Rs is called anomalous
:
; 16
L
4
2
I=1,2
Thestep.
longitudinalat
H coefficient=that
0 is ishaviour is also obtained
forwesmall✓ limit,iswhen<< r02 . Noticewhereuse (15)in thethat
last
Thenq the2resistivity
anomalousHallR↵s ⇠ ⇢xx .where q is a coupling, and 2 = 8⇡G and L is the AdS radius and(25)
we set 22 = L = 1
Forhasskew
scaQering2
2
calingbehaviour
,
it
is
good
idea
to
check
whetherour
egime
coherent
optical⇢conductivity
[14]
which
has
a
well
definedDrude
3necessary to make1 the action finite. Explicit1form+µ/
xx
counter term R
which
is
of
S
is writt
c
.
(2
s =

al.: Anomalous Hall effect1541⇢xx = 22 + (1 + µ2 / 2 )2r0 µ ✓The
2 / 2 )tra2✓ y}+direction(1 + µbreaksat the end of this paper.
axion ( I ) which is linear in {x,is shownlimits.
in Figure 3. Figure 3 show the relation between ⇢xx and Rs
aionspecial
symmetryatand
8 resistivity
The longitudinal
Hhence= 0 givesis an e↵ect of momentum dissipation [32]. Instanton density co

4
2
For
small
limit,
Rs ⇠property:
while
⇠from
. non-trivial
Thereforew
lot. For small (large) , Rx ⇠ ⇢2xxthe(⇢the sharptransition
xx charge,
0Noticeaxion
cangenerate/µmagneto-electric
if we ⇢add
magne
xx ).

+ µ are/ rather long so we wrote it in (26) at the end.
given bygenerated. The equations of 1
motion= temperature.
.
(2
regime. This behavior does not dependon⇢the
2
2

xx

2

2

2

2 2

✓ we
+ (1
µ following/ ) formRs ⇠ ⇢xx .
As ansatz to solutions,
use+
the
-2
1
A = a(r)dt +weHhave(xdy ydx) ,For small /µ limit, Rs ⇠ 4 while ⇢xx ⇠ 2 . Therefore
2
The same behaviour is= also
obtainedfor small ✓ limit, thatx,
12 = y,-4
2
Rs ⇠ ⇢has(2
small
xx . coherent optical conductivity [14]with the metricbeta
ansatzregime2drds2 = U (r)dt2 ++ r2 (dx2 + dy 2 ) .
U (r)The same behaviour is also obtained
for small ✓ limit, that is when q 2 << r02 . Notice th-6
8
From the equations of motion, we found exact solution

From

tion

Log[Rs ]r02 6 q
= 8 2:= Rs M0 ,
usion
4
2
2
2
q + r0 ( + µ )0(21)

consider the magneto-electric interaction from holographic point of view.

1.1"

rnal
HalltizaR 0,
the
on a
ular,

beta regime hasHall
optical conductivity[14] which has a well defined Dru
ep.
the smallanomalouscoefficientispins Thenare correlated,addingcharge coherent
carrierchangesthemagnetic
property
H q
Hqq
m
q +H
U (r) = r
+
+
,
2

-8

2

2

0

r

2

2

4r2

4

2 2

20r6

2

6r4

harge transport. In e↵ective field theory approach,electric8qsuch crossing,-3 a(r) = µ -2+
-1
0
2 Hq

1

r
3r
3
1
2
an
be
impliedbyaddingChern-Simon
term
⇠
A
^
F
in
2+1
dimension.
It
where
µ
is
a
free
parameterinterpretedasthechemicalpotentialandqandm are d
Log[
]
xx
R =
.
(22)

and
t, in

3

FIG. 2. Extraordinary Hall constant as a function of resistivity.
The shown fit has the relation Rs $ !1.9. From Kooi, 1954.

0

Disorder
LimitedThermally
Limited

109
Theory vs. experiment in Dirac Fluid
1 of
10graphene
100 1000

0

200
100
Temperature (K)0Science 11 Feb 2016

20

C

16

H

Achim Harzheim, Andrew Lucas,
Subir Sachdev, Philip Kim,*, Takashi Taniguchi, Kenji Watanabe,Thomas A. Ohki5, Kin Chung Fong,*

L/L0

ObservaMon of the Dirac ﬂuid and the breakdown of the Wiedemann-Franz law in
12graphene Jesse Crossno, Jing . Shi, Ke Wang, Xiaomeng Liu,
8

+V

e

H (eV/µm2)

Temperature (K)

C

h
e
h

10
8

-V

6
4
2
0
40

4
0

−6

−4

−2

0

2

60 80 100
T (K)

4

6

n (1010 cm−2)
8

Holography (HYU) to appear
U(1) x U(1)

ÁÁ
ÁÁ
ÁÁ
Á
Á
Á
Á
Á
Á
Á
Á
Á
Á
Á
6
Á
Á
Á
Á
Á
Á
Á
Á
Á
4
Á
Á

FIG. 3. Disorder in the Dirac fluid. (A) Minimum carrier density as a function of temperature for all three sam
ples. At low temperature each sample is limited by disorderAt high temperature all samples become limited by therma
excitations. Dashed lines are a guide to the eye. (B) TheÁ
Lorentz ratio of all three Ásamples
as aÁÁÁfunction of bath tem
ÁÁperature. The largest ÁWF
violationisÁÁÁÁÁseen
in the cleanes
2
Á
Á
Á
Á
Á
Á
Á
Á
Á
Á
ÁÁ
Á Á ÁÁ ÁÁÁÁÁÁÁ
sample. (C) ÁThegate dependence of the Lorentz
ratio
is wel
Á
Á
Á
Á
ÁÁÁ
Á
Á
Á
Á
Á
ÁÁÁ
Á
Á
Á
ÁÁ
ÁÁÁÁÁÁÁÁÁ
Á
ÁÁÁ
ÁÁÁÁÁ
ÁÁÁÁthree
ÁÁÁÁ
ÁÁÁÁÁ
ÁÁÁÁÁÁÁÁ
fit to hydrodynamic
theoryofÁÁÁÁÁÁÁRef.
[5,
6].
Fits
all
ÁÁof
Á
ÁÁÁÁ
ÁÁ
Á
Á
Á
Á
ÁÁ
ÁÁ
Á
Á
ÁÁÁÁÁÁ
ÁÁ
Á
Á
Á
Á
Á
Á
Á
ÁÁ
Á
ÁÁÁÁ
Á
ÁÁÁ
Á
Á
Á
Á
Á
ÁÁÁÁ
Á
Á
Á
Á
Á
Á
Á
Á
samples areto the-4 shown at-260 K. All 0samples return2
4 Ferm
-400
-200
200
400
3 showliquid value (black dashed line) at high density. Inset
the fitted enthalpy density as a function of temperature and#35

Energy

Fidelity approach to
Adiabatic Quantum Computationof hard problems
Jun Takahashi (Univ. of Tokyo)Ĥ( ) = ĤB + (1)ĤP

2 [0, 1]E1
E0
Annealing parameter λEnergy

Fidelity approach to
Adiabatic Quantum Computationof hard problems
Jun Takahashi (Univ. of Tokyo)Ĥ( ) = ĤB + (1)ĤP

2 [0, 1]

E1
E0

Q.

Annealing parameter λWhen AQC is applied to an NP-hard problem,
what is the physical mechanismthat causes the exponentially small gap?

Energy

Fidelity approach to
Adiabatic Quantum Computationof hard problems
Jun Takahashi (Univ. of Tokyo)Ĥ( ) = ĤB + (1)ĤP

2 [0, 1]

E1
E0

Q.

Annealing parameter λ
1
0.95
0.9
0.85

q

When AQC is applied to an NP-hard problem,
what is the physical mechanismthat causes the exponentially small gap?

0.8

A. (so far)0.75

1st order phase transition (-like) phenomena

0.65

0.7

0.6

0

0.05

0.1

0.15

λ

0.2

0.25

1

Main Question

0.8
0.7
0.6

TCR

The 1st-order phase transitions are actuallystrongly sample dependent.
Can we understand them as a whole?
(e.g. a non self-averaging behavior within aspin glass phase?)

0.9

0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4

0.5

λ

0.6

1

Main Question

Method

0.8
0.7
0.6

TCR

The 1st-order phase transitions are actuallystrongly sample dependent.
Can we understand them as a whole?
(e.g. a non self-averaging behavior within aspin glass phase?)

0.9

0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4

0.5

λ

fix: Maximum Independent Set as a NP-complete problem
Stochastic Series Expansion (SSE) + Replica Exchange (λ direction)

0.6

1

Main Question

0.9

The 1st-order phase transitions are actuallystrongly sample dependent.
Can we understand them as a whole?
(e.g. a non self-averaging behavior within aspin glass phase?)

0.8
0.7

TCR

0.6
0.5
0.4
0.3
0.2
0.1

Method

0

0

0.1

0.2

0.3

0.4

0.5

0.6

λ

fix: Maximum Independent Set as a NP-complete problem
Stochastic Series Expansion (SSE) + Replica Exchange (λ direction)
4.5

χF/N

4

Our study suggests thatfidelity susceptibility is so far thebest way to see the sample-averaged
phase transition

N=20,30,60

3.5
3
2.5
2
1.5
1
0.5
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

#36

Numerical study of real-time correlation function
Comparison with analytical results, random-matrix limit
Free disordered system

Sparse randommatrix models

Increasing disorder degrees of freedom

Dense randommatrix model
GUE, GOE, GSE

#37

Fixed Point Matrix Product States and 1+1D
Topological Quantum Field Theory
Alex Turzillo
California Institute of Technology
Based on work with Anton Kapustin and Minyoung You

June 14, 2016

Idea

I Matrix Product States (MPS) efficiently approximate groundstates of 1D gapped local Hamiltonians. Each gapped phaseof these Hamiltonians corresponds to a Fixed Point MPS.
I Lattice TQFT also describes gapped systems at fixed points.
I Idea: build a dictionary between these two frameworks.
I
I

both are classified by the same algebraic data
MPS and parent Hamiltonians arise from the state-sum

Generalizations

I The algebraic data that classifies these theories makes sense

in other categorical contexts ⇒ generalizations
I Idea: passing structured (ie not strictly topological) field

theories through the dictionary returns variants of MPS.
I Equivariant TQFT −→ Symmetric MPS
I
I

describes gapped symmetric phases: SPTs/SETs
twisted sectors and symmetry breaking

I Spin TQFT −→ Fermionic MPS
I
I

describes fermionic phases, eg the nontrivial Majorana chain
related to symmetric MPS by bosonization

#38

#39

Holographic duality from random tensor
arxiv:1601.01694

Construction
Every vertex:
a

e
d

b

c
a

e

= ∑#)567 Tabcde |abcde>= ∑#$….#',)$…)* Ma1a2…an,b1b2...bm|a1a2...an><b1b2...bm|gHaar
b random state in the
product Hilbert space ⌦5i=1 Hicf

Holographic duality from random tensor
arxiv:1601.01694

Properties• RT formula & bulk correction
Hawking-Page transition• Quantum error correction• Correlation spectrum

#40

LM =
L i + L + Lint ,(13)
the controllingi=1,2
parameterof our system
is dual towith
another
neutral field in some non-linear way. T
it requires
the tuning
1,
2 interact
to 1 , 2 with a certain
degreetheof following
fine tuning,such that
we can density
introduce
minimal
Lagrangian
Engineering Holographic Superconductor Phase Diagrams
tal phase diagram.
X
and 1the phase diagram and the scaling
behavior
near theLM quantum=Zhang
L i + L + Lint ,1 Presented
1 by4Yun-Long2
2 2=(@Ini )orderV for( i ),the Vtwo
( i )order= mparameters, be controlled
(14)
i ito
ystem.
by
i i +
i=1,2
2
2
4
CTS-NTU(Centerfor Theoretical
Sciences,
National
Taiwan University)
meter,
thetuning
field
in
some
1 , 2 interact
1 it requires
1 with
1
2
2 2
4
=
(@
)
V
(
),
V
(
)
=
m
+
, density 2016-06-15
(15)
where
—
zhangyunlong001@gmail.com@ YITPe, we2 introduce the following minimal
Lagrangian
24X
1 are given
1 2 2 12
2
4,m the >0.
Theinteraction
terms
between
,
and
by
L
=
L
+
L
+
L
,
(14)
phaseMdiagram 4, that ithe quantum critical
point
with
2= by a dome
int
gMis1Lcovered
(@
)
V
(
),
V
(
)
=
m
+
i
i
i
i
i i
i,
i

2
2
4
ro condensation of i=1,2O2 6= 0, which normally happens in real physical systems.
One
tices that there exists an overlapping
for future studies.
The1
1 2 2 1
1 X phase 2which we left
22
4
2
gM Lrefer= to the (@)
V ( ),
V( )= m+,Lint
= of parameters
Fi (in )ouri ,second model(16)
motivation gofMthechoicesschematic
2 point at
2
4m on the scaling symmetries2 inAppendix C, where the quantum critical
i=1,2
urce 1J can emerge
a nature V-shape area at thetemperature.
1 finite
1
2
2 2
4
2
2
=
(@ i )V ( i ),with
V (mii), =m+(15)m < i0 iand i ,i i , > 0. The interaction
terms between 1 , 2 and
2
2
4

=

1
(@ )2
2

Δ+
[� � /(μ� ) � ]× ����7

V ( ),

1 2 2 1
V( )= m+2
4pling constant, m2i , m2 < 0 and i ,e given by
1X
2
gM Lint =Fi ( ) i2 ,2 i=1,2
�

�

4

,

Δ+
[�� /(μ� ) � ]× ���> 0. The interaction terms
����X

2 i=1,2����Fi ( ) i2 ,

����

7

����

�

�

(16) 1
2
gM Lint =

����

(17)

����
����

of the coupling function Fi ( ) will be given later. Di↵erent Fi ( )at the condensation of 1 and 2 are controlled by via shifting
onsequently, di↵erent phase structures arise. We will work in the2
2
fields, namely
2/g
0. Jiunn-Wei Chen, Shou-Huang Dai, Debaprasad Maity, Yun-Long Zhang
arXiv:
1603.08259
M !
4: The phase
diagramof modelII arounda natural quantum critical point. It
Figure10: Left: the 3D schematic diagram of Figure 4
ion forscalarturn2 (orange)out towith
be coupling functions
densityplotthephase
1(blue)fields
and phase
F1 ( ) =Constraints in Rindler Fluid & AdS Cutoff Fluid
arXiv: 1207.5309 & 1401.7792 & 1408.6488
Extremal Case

AdS2 /CFT1

Near Horizon

Cutoff AdS /Near Boundary

Effective Fluid？

AdS /CFT&CMT

Finite Temperature

Rindler /Special Fluid？

Cut-off
Horizon

CFT

=

T
M
C

Near Rindler

MembraneBlack HolesAdS Black Brane

Condensed Matter

Presented by Yun-Long Zhang (zhangyunlong001@gmail.com)