Oral Session A2 (Tuesday, February 13)
Chair: Stefan Blügel,Peter Grünberg Institute and Institute for Advanced
Simulation, Forschungszentrum Jülich GmbH

Keynote Talk
14: 00 - 14 : 40

Prineha Narang
Physical Sciences, the University of California, Los Angeles (UCLA)

TBD

Contributed Oral
14 : 40 - 15: 00

Hyperuniform electron distribution in quasicrystals
Shiro Sakai

RIKEN Center for Emergent Matter Science, Japan

Electrons in a quasiperiodic potential or lattice are distributed in an aperiodic but regular manner. Althoughelectron wavefunctions in such a system often show multifractality, other physical quantities do not necessarily
have multifractal distribution. For instance, the charge distribution on a Penrose lattice is not multifractal but
hyperuniform [1].
Hyperuniformity [2] is a framework to quantify the regularity of a point distribution in a d- dimensional space.
Counting the number of the points inside a window of radius R, we define its varianceσ2 (R) as the window
moves over the space. The distribution withσ2 (R) < O(Rd) is called hyperuniform, as it is more uniform than arandom distribution. Several diﬀerent hyperuniformity classes have been identified.
Using a generalization of the hyperuniformity framework to scalar fields [2], we studied a one-dimensional
Aubry-Andre-Harper model in terms of hyperuniformity [3]. The charge distribution of this model was foundto be either class-I or class-II hyperuniform depending on the model parameters. By calculating the total energy,
we found a phase transition between the regions of diﬀerent hyperuniformity classes. This is a transition between
two diﬀerent non-uniform charge distributions in the absence of translational symmetry

Referemces[1] S. Sakai, R. Arita, and T. Ohtsuki, Phys. Rev. B 105 (2022), 054202.
[2] S. Torquato, Phys. Rep. 745 (2018), 1.
[3] S. Sakai, R. Arita, and T. Ohtsuki, Phys. Rev. Research 4 (2022), 033241.

Oral Session A2 (Tuesday, February 13)
Chair: Stefan Blügel,Peter Grünberg Institute and Institute for Advanced
Simulation, Forschungszentrum Jülich GmbH

Contributed Oral
15: 00 - 15: 20

Four-index coulomb interaction beyond Hund’s couplingSteﬀen Backes
RIKEN iTHEMS

To study the properties of strongly correlated electron materials one usually employs an eﬀective
low-energy lattice model, such as the Hubbard model, to obtain a simplified description of thematerial under consideration. Such a model is fully defined by the kinetic, or electron-hopping term,
and the interaction term, originating from the electron-electron Coulomb interaction. This
interaction term is a two-particle operator and in general involves the interaction of 4 diﬀerent
electron channels. For highly symmetric orbital basis functions this term is sparse and involves
terms like the density-density interaction, or pair-hopping and spin-flip terms induced by the Hund’scoupling. Even though in real materials all 4-index terms can in principle provide a finite
contribution, they are usually assumed to be small and thus neglected for most practical
calculations.
In this talk we will discuss the symmetry constraints imposed by the symmetry group of thecorresponding atom on the form of the Coulomb interaction, and how the resulting non-zeroelements can be obtained for specific systems. Using the constrained random-phase approximation
we will present ab-initio 4-index elements of the Coulomb interaction for real materials and discusscases where they show a non-negligible eﬀect on the electronic structure. Using exact
diagonalization of finite systems and the dynamical mean-field theory for lattice models and realmaterials, we will present the impact of these terms on electronic properties such as the spectral
function.

Contributed Oral
15: 20 - 15: 40

Exact quantum spin Hamiltonian for magnetic interactions
H. Katsumoto1, F. Lux2, Y. Mokrousov1,3, and S. Blügel1

Oral Session A2 (Tuesday, February 13)
Chair: Stefan Blügel,Peter Grünberg Institute and Institute for Advanced
Simulation, Forschungszentrum Jülich GmbH

1 Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Germany
2 Department of Physics, Yeshiva University, USA
3 Institute of Physics, Johannes Gutenberg-University Mainz, Germany

The intricate nature of magnetism arises from the interplay of Heisenberg interactions and higher-orderexchange interactions [1, 2]. The awareness is rising that the higher-order exchange interactions depend not
only on the number of magnetic sites N but also on the local spin magnitude S. Nevertheless, a definitive
method for uniquely deriving a spin Hamiltonian that comprehensively captures these interactions for agiven system remains elusive.
his presentation is dedicated to delving into the algebraic aspects of the spin-permutation operator oﬀering amethodology for deriving an exact quantum spin Hamiltonian tailored for an N- site system of spin S. We
showcase the construction of the exact quantum spin Hamiltonian of S = 1/2 and 1 and extending to higherorder interactions up to 4-site systems. Furthermore, we delve into higher-order terms related to scalar spinchirality using this algebraic approach. he magnetism in solid materials is described by the classicalization of
the quantum spin Hamiltonian.
hese findings not only contribute to our understanding of magnetism in solids but also bear relevance tonuclei and cold atom systems.
We acknowledge funding from the ERC grant 856538 (project "3D MAGIC”), the DeutscheForschungsgemeinschaft (DFG) through SPP-2137 and SFB-1238 (project C1).
References[1] M. Hoﬀmann et al., Phy. Rev. B 101, 024418 (2020).
[2] S. Grytsiuk et al., Nat. Commun. 11, 511 (2020).