Hard-core bosonic DMFT study on spin-state transition in LaCoO3T. Okauchi, J. Kuneš2, and A. Hariki1
1Department of Physics and Electronics, Graduate School of Engineering, Osaka Metropolitan University, Sakai 599-8531, Japan
2Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria

We study spin-state transition in LaCoO3 using ‘bosonic’ dynamical mean field theory (B-DMFT). The spin excitations of LaCoO3 can be viewed as a collection of mobile
spin-triplet excitons which obey a hard-core (HC) constraint. One-particle DMFT self-energy is ill-defined in the HC constraint, leading a numerical difficulty to achieve aDMFT self-consistent condition. To solve this, 1) we adopt a Dyson-Mori formalism in computing the self-energy and 2) develop a continuous-time quantum Monte Carlo
impurity numerical solver implementing a broken commutation relation by the HC constraint. To test our methodology for HB-DMFT, we calculate a phase diagram of twodimensional two-band Hubbard model, allowing a staggered order of boson densities that corresponds to a spin-state order (SSO) in the electronic system. We discuss afuture plan for an application of the HB-DMFT method to a more realistic model of LaCoO3.

Introduction: LaCoO3

Method: DMFT for hard-core bosons
Co3+(3d6): atomic picture

Susceptibility
K. Asai et al. JPSJ 67 290 (1988)

Low spin(LS: S=0)

IS? HS?

BDMFT: Anderson impurity modelIntermediate(IS: S=1)

High spin(HS: S=2)† †[bi, bj] = [bi , bj ] = 0

Δ(τ)

eg
Hund10Dq

Hardcore constraint (HC)

Impurityt2gsite†[bi, bj ] = δij(1 − 2ni)ΦDynamic and kinematic HC constraintact in different Hilbert space

Intermediate spin

＜LSBroken sum rule of spectrum

Green function for HC bosons+∞

1−ImG(ω)dω = 1π ∫−∞＜High spin
Low spin

Upper1G(ω) =ω − hloc − Δ(ω) − Σ(ω)
Break the sum rule

Hubbard bandQuestionΓḠ(ω) =ω − hloc − Δ(ω) − Σ(ω)

LS to HS thermal transition Co3+ in atomic picture?

Experiment

TheoryvsTomiyasu et al. PRL 119, 196402 (2017)

M. Karolak et al. PRL 115, 046401 (2015)

HSMessages■ No experimental evidence ofLS

1−ImḠ(ω)dω = Γπ ∫−∞Absent in HC∞∞+∞

Self energy (atomic model)
anomalous behavior
in high frequency

Definition of rescaling factor ΓHS-LS long-range ordering1Γ≡−dω Ḡ(ω) = 1 −dωa(ω)∫−∞π ∫−∞■ Spin-state transition beyond
the atomic picture

Messages

Excitonic picture: mobility of IS
Mobility of intermediate spin

Co3+(3d6): excitonic picture

LSA. Sotnikov et al. Sci. Rep. 6, 30510 (2016)

excitonHSIS
holec

Problem on HB-DMFT:

Solution for this problem:• Self energy ill-defined with HC• Numerical difficulty for achievingDMFT self-consistent condition• Use Dyson-Mori form of the GF• Apply HC to the CT-QMC solver forauxiliary Anderson impurity modeleg x -y2tegt2gĤ =2one exciton

vacuumxyyzzx

IS(T1g) exciton

tt2g

ISLS
Strong attractive interaction
ISxz

ISyz

−VHS(T2g) bi-excitonnî ,αOn-site energy

Dynamical HC constraint

∑
it2g

∑∑i

αnî ,1nî ,2Local attraction term

holeHSzdx -z
22ISxzISxz

ISyz

Propagate in zx planeQuestion

HSz+tb̂†±∑ i δ1,1i,δ1b̂i,1 +b̂†±∑ i δ2,2i,δ2

Flavor-diagonal and direction-dependent
hopping term

Spectral density (with HC)

Occupation vs attraction V■ Large dispersion of IS

V = 590 meV■ Two IS excitons into one HSt2g

E = 2ϵISVz■ Strong attractive V in LaCoO3

Ĥ = ϵIS∑∑αinî ,α − V

On-site energy+t

∑∑
i

α,β∑∑
i α>βnî ,αnî ,βLocal attraction term

(1 − δαβ)b̂†±i eβ,α|xy〉

𝔉(eV)b(eV)|xy⟩, |yz⟩, |zx⟩

| ·|zx〉· · , IS, IS, · · ·V
ISx ISxz
ISy ISyz y

Flavor-diagonal and direction-dependent hopping termeg

cexcitonBhas
flavors:
PHYSICALISREVIEW
101,3245162(2020)|yz〉

b̂i,αSite2

Theory: attractive bosonic Hubbard model

Attractive bosonic Hubbard model
ARIKI et al.

V = 615 meV

Site1

exciton (immobile bi-exciton)
E = ϵHS = 2ϵIS − Vb̂i,2Spin-state order appears by the on-site attraction V (HS excitation)?

ImmobileMessageseg(Fixed: β = 40 eV-1, t = 0.116 eV, εIS = 0.34 eV)

U+nî ,α(nî ,α − 1)∑∑
2 i αϵISbi-excitoneg electrondxz

aResult: calculation under spin-state order
2D 2-flavor Hubbard model3z2-r2sbx■ SSO appears spontaneously by Vpropagatingeach| · · · , inLS,HS,plane···HSHSzzForming HSby local attraction
Vegy■ Explicit HC corresponds to U → ∞■ Our methodology for HB-DMFT is
implemented properlyFuture workx

Application of HB-DMFT to a realistic model of LaCoO3 1) including full IS
degrees of freedom and 2) extracting parameters from ab-initio calculationa