Antoine Georges (Flatiron Institute and Collège de France): Strong Electronic Correlations: the Hund Metals Route

The proximity to a Mott transition and the Kondo effect in heavy fermion compounds are two classic mechanisms leading to strong electronic correlations. In this talk, I will highlight an alternative route to strong correlations in which Hund’s rule coupling plays the key role. Remarkably `Hund metals’ are both strongly correlated and quite itinerant. A broad class of materials can be characterized as Hund metals, ranging from iron-based superconductors to transition metal oxides such as Sr2RuO4. The latter is also an important testbed for quantum many-body methods aiming at understanding the physics of strong electronic correlations in real materials. Dynamical Mean Field Theory (DMFT) provides the appropriate conceptual and computational framework to understand Hund metals, and has played an essential role in revealing this new route to strong electronic correlations.

 

 

Young-Woo Son (KIAS): Relativistic ab initio extended Hubbard interactions

For massive database-driven materials research, there are increasing demands for both fast and accurate quantum mechanical computational tools. Contemporary methods can be fast, sacrificing their accuracy, or be precise, consuming a significant amount of resources. In this talk, to overcome such a problem, I will present my group’s recent efforts on systematic improvements of self-interactions error corrections in approximated exchange-correlation functionals commonly used for first-principles calculations based on density functional theory (DFT). I will present theories on efficient ways of computing position-dependent self-consistent on-site and inter-site Hubbard interactions and their fully relativistic extension [1-3]. Owing to a low computational cost of the new method comparable to DFT and improved accuracy to the GW approximation, the new method provides an opportunity to study the correlated solids in large scale structures and full phase space of interests. A few examples [4-7] obtained using newly implemented subroutines within conventional first-principles codes will be demonstrated to show superior performance of our new method.

[1] S.-H. Lee and Y.-W. Son, Phys. Rev. Res. 2, 043410 (2020).

[2] W. Yang et al., Phys. Rev. B 104, 104313 (2021).

[3] W. Yang and Y.-W. Son, in preparation (2023).

[4] J. Huang et al., Phys. Rev. B 102, 165157 (2020).

[5] W. Yang et al., J. Phys. Condens. Matter 34, 295601 (2022).

[6] B. G. Jang et al., Phys. Rev. Lett. 130, 136401 (2023).

[7] N. Tian et al., arXiv:2211.08114.

 

 

Hunpyo Lee (Kangwon National University): Accelerated Variational Eigensolver on D-Wave Quantum Annealer

D-Wave quantum annealer displays significant potential due to the recent paid increase in qubit capacity. In addition, it has been extensively applied to solving combinatorial optimization problems requiring an annealing process for exact energy of ground state and for the research of the Ising model.

In this talk, I will shortly introduce the D-Wave Advantage machine on Pegasus graph with 5000++ qubits and discuss limitations by embedding. I also present the recent results obtained from D-Wave Quantum Annealer and simulated annealing approach on frustrated Ising model. Finally, I will introduce hybrid acerated variational eigensolver approach to find minimum of continuous objective function.

 

 

Kwon Park (KIAS): Solving high-temperature superconductivity with quantum computers: Efficient quantum algorithm for resonating valence bond and spin liquid states

High-temperature superconductivity is the holy grail of quantum many-body problems with a seemingly unsurmountable obstacle of the exponentially increasing Hilbert space as a function of the system size. Realizing Feynman’s vision of quantum simulation, high-temperature superconductivity is a perfect example that can benefit from quantum computers. For the success of the quantum simulation, however, it is of critical importance to prepare a good trial state that can have a sizable overlap with the exact ground state. In this talk, we would like to show that, serving as a good trial state for high-temperature superconductivity, the resonating valence bond state can be prepared by using the efficient quantum algorithm implementing the Gutzwiller projection via the fixed-point amplitude amplification method. This method can be applied to various different types of the spin liquid state formulated in the form of the Gutzwiller-projected Fermi Sea.

 

 

Ara Go (Chonnam National University): Identification of the magnetic order from electronic structure

The identification of magnetic states in materials is a topic of significant interest across various fields. However, the direct identification process is not always straightforward due to limitations in neutron scattering experiments. In this study, we introduce a machine-learning approach that utilizes decision-tree algorithms to identify magnetism based on the spin-integrated excitation spectrum, specifically the density of states. To create our dataset, we performed Hartree-Fock mean-field calculations on potential antiferromagnetic orders using a Wannier Hamiltonian derived from first-principle calculations focused on BaOsO3. Our machine learning model was trained on diverse spectral data, encompassing the local density of states, momentum-resolved density of states at high-symmetry points, and the lowest excitation energies relative to the Fermi level. While the density of states exhibited promising performance for machine learning, we discovered that the broadening method significantly influenced the model's effectiveness. To enhance the model, we incorporated the excitation energy as a feature for machine learning, resulting in outstanding classification of antiferromagnetic order, even when tested on samples generated by different methods than those used for training. Furthermore, we applied the model to dynamical mean-field results, which were obtained using a completely distinct computational method, and observed favorable accuracy. This successful application suggests the potential applicability of our model to more realistic data.

 

 

HyoWon Park (UIC): First-principle study of the spin/charge susceptibility in strongly correlated materials

Understanding the relationship between the strongly correlated electronic structure and its collective behavior in materials has been a grand challenge in condensed matter physics. Co-intercalated NbS2 (Co1/3NbS2) shows a novel transport property exhibiting a large anomalous spin Hall effect, however the origin of such phenomena has been unclear. Here, we show that novel non-coplanar antiferromagnetic ordering is favored in Co1/3NbS2 from first-principle and the calculated anomalous Hall conductivity is extremely large, which is consistent with the experimental measurement. In particular, we find that the spin susceptibility and the correlate band structure in Co1/3NbS2 calculated using dynamical mean field theory (DMFT) are consistent with the 3q magnetic structure of this material as expected from the non-coplanar antiferromagnetic ordering. We will also show that the charge susceptibility calculations in rare-earth tellurides (RTe3) based on the Fermi surface nesting obtained from first-principle can explain the experimental trend of charge ordering peaks measured in these materials across different rare-earth ions.

 

 

Minjae Kim (KIAS): Orbital Selective Electronic Correlations and Topological Superconductivity of Iron Chalcogenide: A DMFT perspective

The iron-based superconductor, FeSe1-xTex (FST), obtained significant attention due to two emergent phenomena of the material. The first is the topological superconductivity hosts Majorana Fermion in its boundary as a candidate of the topologically protected quantum bit [1,2]. The second is the orbital selective Mott transition, which is a selective localization of the Fe(dxy) orbital while other orbitals, including Fe(dxz/yz), remain as itinerant [3]. This talk shows that the topological superconductivity and the orbital selective Mott transition are intimately connected in the FST material [4]. We use the state-of-the-art linearized quasiparticle self-consistent GW plus dynamical mean-field theory framework with spin-orbit coupling (LQSGW+DMFT+SOC), which enables the quantitative description of the topological Dirac surface state of the FST material. We show that the topologically non-trivial band, the Fe(dxy) orbital origin, experiences a localization from the orbital selective Mott transition. This identification shows that the non-trivial Z2 topology for the topological superconductivity could be realized only for the physical regime that is not too far but not too close to the orbital selective Mott transition. This observation enables understanding and manipulation of the topological superconductivity of iron-based superconductors. Also, the strong electronic correlation at the topological surface state can be the origin of the experimentally observed time-reversal symmetry breaking at the surface of the FST material [5].

[1] G. Xu et al., PRL 117, 047001 (2016),

[2] P. Zhang et al., Science 360, 182 (2018)

[3] M. Yi et al., Nat. Comm. 6, 1 (2015)

[4] Minjae Kim et al., https://arxiv.org/abs/2304.05002 (2023).

[5] C. Farhang et al., PRL 130, 046702 (2023)

 

 

Sangkook Choi (KIAS): Harnessing DMFT: recent advances in Hund Metal Research

The on-site Hund coupling J has been a focal point of research in electron correlation for the past 15 years. It leads to the emergence of a Hund metal, a correlated metallic regime that occurs in multiorbital systems away from half-filling. This system is characterized by electron correlation promoted by J rather than proximity to a Mott insulator, resulting in a range of physical phenomena such as spin-freezing crossover, spin-orbital separation, orbital differentiation, and superconductivity.

In this talk, we will provides an overview of the Hund metallic phase and highlights our recent discoveries in the field [1,2,3]. These include the existence of Hund metals in two orbital systems, an enhancement of charge-order instability in the Hund metallic regime, and key experimental signatures of Hund metal. We will also introduce recent advances in ab initio DMFT methodology developments targeting correlated quantum materials[4,5,6].

[1] S. Ryee, M. J. Han, and S. Choi, Phys. Rev. Lett. 126, 206401 (2021).

[2] S. Ryee, P. Sémon, M. J. Han, and S. Choi, npj Quantum Mater. 5, 1 (2020).

[3] S. Ryee, S. Choi, and M. J. Han, arXiv:2207.10421

[4] S. Choi, P. Semon, B. Kang, A. Kutepov, and G. Kotliar, Comp. Phys. Comm. 244, 277 (2019)

[5] S. Choi, A. Kutepov, K. Haule, M. van Schilfgaarde, and G. Kotliar, npj Quantum Materials 1, 16001 (2016)

[6] B. Kang, C. Melnick, P. Semon, S. Ryee, M. J. Han, G. Kotliar, and S. Choi, arXiv:2007.14610

 

 

Yuta Murakam (Riken): Quasi-equilibrium approach for photo-doped Mott insulators

Doping charge carriers into Mott insulators provides a pathway to produce intriguing emergent phenomena. In equilibrium systems, doping can be chemically controlled. On the other hand, photo-doping, where particles are excited across the Mott gap, provides an alternative way. Compared to chemical-doping, photo-doping creates a wider variety of charge carriers, which may lead to the emergence of fascinating nonequilibrium states. In particular, when the gap is large, the life-time of photocarriers is exponentially enhanced, which can lead to metastable states after the intraband cooling of photo-carriers.

In this talk, we introduce the quasi-equilibrium description of such metastable states [1] and reveal the nature of these states in the one-dimensional (1D) photo-doped extended Hubbard mode [2]. In the one-band Hubbard model, photo-doping creates no-occupied sites (holons) and doubly occupied sites (doublons), which are charge carriers of the system. Firstly, we point out that the Schrieffer-Wolff transformation allows us to separate the effects of the virtual and real recombination processes of charge carriers. Then, we introduce the quasi-equilibrium approach of the photo-doped system using the effective model derived from the Schrieffer-Wolff transformation and chemical potentials for doublons and holons (Generalized Gibbs ensemble description). We demonstrate a numerical analysis using the infinite time-evolving block decimation (iTEBD). Secondly, we discuss the analytical aspect of photo-doped states in the 1D Hubbard model. We show that the corresponding wave function in the larger on-site interaction limit can be expressed as |Ψ⟩ = |Ψcharge⟩|Ψspin⟩|Ψη−spin⟩, which indicates the separation of spin, charge and η−spin degrees of freedoms. Here η−spin represents the type of the photo-carriers. This state is analogous to the Ogata-Shiba state of the doped Hubbard model in equilibrium. The expression allows us to identify the metastable η-pairing and charge-density-wave (CDW) phases. The η-pairing phase hosts a quasi-long range order associated with the condensation of pairs with momentum π. The CDW phase is characterized by the string order as the Haldane phase. Our results demonstrate that the emergent degrees of freedom activated by photo-doping can lead to peculiar types of quantum states absent in equilibrium.

[1] Y. Murakami, S. Takayoshi, T. Kaneko, Z. Sun, D. Golež, A. J. Millis, P. Werner, Comm. Phys. 5, 23 (2022).

[2] Y. Murakami, S. Takayoshi, T. Kaneko, A. Lauchli, P. Werner, Phys. Rev. Lett. 130, 106501 (2023).

 

 

Seung-Sup B. Lee (SNU): Multipoint correlation functions: spectral representation, numerical evaluation, and improved estimator

Multipoint correlation functions describe the many-body processes relevant to transport properties (e.g., vertex corrections to the conductivity) and spectroscopy (e.g., inelastic scattering of photons and neutrons). However, the non-perturbative computation of multipoint functions for strongly correlated systems at low temperatures, especially on the real-frequency axes, has been notoriously challenging. In this talk, I will present some recent breakthroughs made by my colleagues and me. We have derived the generalized spectral representations of generic multipoint functions that encompass all many-body formalisms (zero-temperature, Matsubara, and Keldysh) for the first time [1], and developed the numerical renormalization group (NRG) method for computing local multipoint functions of quantum impurity systems by evaluating such spectral representations [2]. Very recently, we have devised the symmetric improved estimator for three- and four-point functions [3]. With these, we can now compute real-frequency multipoint functions for strong interactions and low temperatures with high accuracy, which goes beyond the reach of the other approaches.

[1] F. B. Kugler*, S.-S. B. Lee*, and J. von Delft, Phys. Rev. X 11, 041006 (2021). (*: equal contributions)

[2] S.-S. B. Lee, F. B. Kugler, and J. von Delft, Phys. Rev. X 11, 041007 (2021).

[3] J.-M. Lihm, J. Halbinger, F. B. Kugler, J. Shim, J. von Delft, and S.-S. B. Lee, in preparation.

 

 

Steffen Backes (University of Tokyo): Relevance of 4-index Coulomb interaction terms beyond Hund’s coupling

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 the material 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 only involves density-density interaction terms and pair-hopping and spin-flip terms induced by the Hund’s coupling. 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 origin and physical relevance of these terms, and their implications on the electronic properties. Using the constrained random-phase approximation we will present ab-initio 4-index elements of the Coulomb interaction for real materials and discuss cases 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, we will present the impact of these terms on electronic properties such as the spectral function.

 

 

Alexei Andrenov (IBS-PCS): From Dyson Models to Many-Body Quantum Chaos

Understanding the mechanisms underlying many-body quantum chaos is one of the big challenges in theoretical physics. We tackle this problem by considering a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows to disambiguate between operator growth and emph{delocalization}, showing that the latter is the dominant process in the single-particle to many-body chaotic transition. Our results (arXiv:2302.00917) are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians, in this case up to dimension 2^19 x 2^19. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.

 

 

Aaram J. Kim (DGIST): Symmetry-restoring homotopic action

We present the theory of symmetry-restoring homotopic action with the proof-of-principle example 2d Hubbard model. By explicitly breaking the existing symmetry of the original action at the reference system and expanding with respect to the symmetry-restoring and many-body interaction term, one can achieve the improved convergence in the diagrammatic series. Furthermore, we show that the freedom of choosing the dependence of the symmetry restoring term on the expansion parameter allows one to tame dangerous long-order oscillations, inherent in symmetry-restoring expansions, with controlled error bars. We access low-temperature strong-coupling regime of the half-filled 2d Hubbard model with large antiferromagentic correlation length, and observe the Slater- to-Mott Hubbard crossover in a numerically exact way.

 

Hyun-Yong Lee (Korea University): Dipole Condensations in Tilted Bose-Hubbard Chains

We study the quantum phase diagram of a Bose-Hubbard chain whose dynamics conserves both boson number and boson dipole moment, a situation which can arise in strongly tilted optical lattices[1]. With DMRG simulations, we show that the conservation of dipole moment has a dramatic effect on the phase diagram. In particular, various types of incompressible dipolar condensate phases arise in the thermodynamic limit. In finite-sized systems however, it may be possible to stabilize a ‘Bose-Einstein insulator’: an exotic compressible phase which is insulating, despite the absence of a charge gap. We also suggest a cold atom experiment that may identify these exotic phases.

[1] E. Lake, H.-Y. Lee, J. H. Han an T. Senthil, arXiv:2210.02470

 

 

Se Young Park (Soongsil University): Electronic ferroelectricity in the site-dependent one-dimensional Hubbard-Holstein model

Electronic ferroelectrics are a class of materials having switchable polarization dominantly contributed by electron transfer in the switching process. In many electronic ferroelectrics, the inversion-breaking orderings are induced by an intimate coupling between the electronic degrees and other degrees of freedom, such as electronic-phonon coupling stabilizing the inversion-breaking charge disproportionation. In this talk, we investigate the one-dimensional Hubbard-Holstein model, where the site-dependent sign change in electronic-phonon coupling enhances the ferroelectric phase driven by charge ordering. By calculating electronic structures using the density-matrix renormalization group, we obtain the phase diagram of this modified one-dimensional Hubbard-Holstein model as a function of the on-site and inter-site Coulomb interaction and electron-phonon coupling. We find that the charge-order-driven ferroelectric phase is stabilized in a wide range of parameters where polarization is dominantly contributed by electronic transfer between the sites. The candidate systems that could exhibit the identified electronic ferroelectricity will be discussed.

 

 

Hyoung Joon Choi (Yonsei University): Electronic structure of twisted graphene layers

Magic-angle twisted bilayer graphene (MA-TBG) has tunable electronic and magnetic properties by the twist angle and the doping. However, it is very expensive to fully investigate its electronic and magnetic properties from the density functional theory (DFT) because its moiré supercell contains more than ten thousand atoms. Here, we develop an efficient self-consistent method to calculate electronic structures near the Fermi energy of doped MA-TBG with almost continuous change of doping concentration [1]. Our method is based on spin-unpolarized DFT results of undoped MA-TBG and a few doped ones. With this method, we obtain doping dependences of low-energy electronic band structures and spin and valley properties of MA-TBG. We obtain ferromagnetic phase diagram of MA-TBG as a function of doping and temperature. We also discuss spin-valley polarizations of MA-TBG as a function of doping.

[1] Yosep Cho, Young Woo Choi, and Hyoung Joon Choi, in preparation.

 

 

Choong H. Kim (IBS-CCES): Hund correlations in single-layer ruthenate thin films

Hund's coupling, instead of Hubbard interaction, is a new knob to manipulate the physical properties of strongly correlated materials. For example, the role of Hund's coupling in unconventional superconductors such as Fe-pnictide or Sr2RuO4 has been re-examined from the perspective of the newly proposed correlated metallic phase called Hund's metal. Among them, ruthenates have an appropriate size of Hubbard interaction and Hund's coupling, making them a suitable system for studying Hund's correlation physics. In particular, when ruthenates are grown as a single-layer thin film, bandwidth, crystal field, etc. can be effectively controlled, and various emergent phases can be observed. In this talk, we present a systematic theoretical study on the novel metallic and insulating properties of various ruthenates films by means of density functional theory plus dynamical mean-field theory (DMFT). Our study newly suggests the possibility of ruthenate film as a new platform to study the characteristics of Hund correlation.