Session D08: Advances in Computational Techniques for Strongly Correlated Systems

Machine learning force-field model for phase separation dynamics in Jahn-Teller models for manganites

We present a scalable machine learning (ML) force-field model to explore the large-scale dynamics of Jahn-Teller coupling between the electronic e_g orbitals  and  the molecular tetrahedral distortions in manganites. While the equilibrium properties of the electronic JT model have been extensively studied before, to the best of our knowledge, the phase-ordering dynamics of this important model remains unexplored. As the driving forces on the local lattice distortions come from the electron degrees of freedom, their calculation requires solving the electron band structure at every time-step of the simulation, which could be prohibitively expensive for large systems. Assuming the principle of locality for electron systems, a neural-network model is developed to accurately and efficiently predict local electronic forces with input from lattice degrees of freedom in the immediate neighborhood. Our ML-enabled large-scale thermal quench simulations of hole-doped systems uncover anomalous phase separation phenomenon intertwined with unusual coarsening dynamics of antiferromagnetic lattice distortion. Our work opens new avenues for multi-scale dynamical modeling of correlated electron systems.   

2D MPS-DMRG: Quantum dimer model on a two-dimensional quasicrystal

Complex many-body quantum systems constitute many of the most interesting topics in physics, from quantum spin chains to frustrated magnets to quantum dimers and loops originally introduced to model high-temperature superconductors. But such phases are notoriously difficult, owing to the exponential scaling of Hilbert space, with the problem increasingly difficult in higher dimensions. Variational methods such as MPS-DMRG (matrix product state density matrix renormalisation group) offer access to low-lying energy states of such interacting systems, for example finding the ground states of large 1D many body systems to high accuracy. However, DMRG has found limited application in 2D or higher.

We successfully apply MPS-DMRG to quantum dimer model on large 2D systems, approximating the thermodynamic limit. The method is made tractable by placing the models on a modification of the Ammann Beenker tiling. Bearing the symmetries of a physical quasicrystal, the tiling features long-range order without periodicity. The dimer models combine with these symmetries so as to admit degrees of freedom similar to those in 1D ladders. We present an overview of ordered phases, phase transitions, entanglement entropy, and onsite and long-range correlations. 

This work is with Felix Flicker and Natalia Chepiga.    

Three-body Fermi-liquid effects on transport through the U=∞ Anderson impurity

We investigate the impact of three-body Fermi-liquid corrections on the transport through an Anderson model with N degenerate levels. Specifically, we consider the strong interaction limit where U=∞ and the occupation number n_d of the impurity levels varies in the range 0<n_d<1, which includes the Kondo and the valence fluctuation regimes, depending on the level position ε_d. The three-body correlations among the impurity electrons emerge in the case where the system does not have the electron-hole and the time-reversal symmetries. They have recently been shown to play an essential role in the next-leading order terms of transport coefficients at low energies, together with the other well-known Fermi-liquid parameters such as the phase shift, the Wilson ratio, and the renormalization factors [1-3]. We calculate the next-leading order terms of the nonlinear conductance, the current noise, and the thermal conductance for quantum dots with N=4, using the numerical renormalization (NRG) approach. In our presentation, we will provide an overview of the NRG results and discuss the implications of the three-body effects. [1] A. Oguri, and A. C. Hewson, PRL 120, 126802 (2018). [2] M. Filippone, C. Moca, A. Weichselbaum, J. von Delft, and C. Mora, PRB 98, 075404 (2018). [3] C. Mora, P. Vitushinsky, X. Leyronas, A. A. Clerk, and K. Le Hur, PRB 80, 155322 (2009).   

Unbiased fluctuation diagnostics of the self-energy: pseudogap physics beyond spin fluctuations

Correlated electronic systems may give rise to multiple effective interactions, whose combined impact on quasiparticle properties can be difficult to disentangle. We introduce and apply an unambiguous decomposition of the electronic self-energy, which allows us to quantify the contribution of various effective interactions simultaneously. We use this tool to revisit the hole-doped Hubbard model at strong coupling within the dynamical cluster approximation, where spin fluctuations have been identified as the origin of the pseudogap. While our fluctuation diagnostics confirms that spin fluctuations indeed suppress antinodal electronic spectral weight, we show that they alone can not capture the pseudogapped self-energy quantitatively. Other nonlocal Feynman diagrams yield substantial contributions and are needed for a quantitative description of the pseudogap.   

Perturbative Solution of Fermionic Sign Problem in Lattice Quantum Monte Carlo: A Cuprate Case

We developed a strong coupling perturbation scheme for general Hubbard model around half-field particle-hole symmetric reference system. The approach based on a lattice determinatal Quantum Monte Carlo method in continuous and discrete time versions for a large periodic clusters in a fermionic bath. The first order perturbation in the shift of chemical potential and long-range hopping gives a reasonable accuracy for parameters corresponding to the optimally doped cuprate systems. We calculate spectral function of hole doped  t-t'-U  model for interaction strength equal to the band width and discuss a mechanism of the pseudogap formation. Results for standard cuprates model with U=8t=W and t'/t=-0.3 for temperatures of the order of T=0.1t show formation of the pseudo-gap and Fermi-arcs. We discuss the magnetic and superconducting instability using symmetry broken external fields.   

Diagrammatic analysis of Anderson's orthogonality catastrophe

The study of the Fermi-edge singularity in x-ray absorption spectra of metals is a paradigmatic fermionic model, which exhibits logarithmic divergences in perturbation theory. Thus, it offers a playground for different diagrammatic approximations. It has been shown that a summation of parquet diagrams and, even more restricted, a 1-loop fRG approach are sufficient to include all leading-logarithmic terms of the model. Our motivation is to investigate the model beyond that and give a diagrammatic description of Anderson's related orthogonality catastrophe. For this, we developed a parquet solver using Matsubara formalism, which includes all components of the four-point vertex in a theory with two particle types. The recently introduced single-boson exchange (SBE) decomposes the four-point vertex into diagrams with lower frequency dependences simulating effective bosonic interactions. We make use of the SBE decomposition and show that multi-boson exchange (MBE) diagrams need to be taken into account in order to correctly include all the leading-logarithmic contributions of the model.   

Active orbital degree of freedom and potential spin-orbit-entangled moments in the Kitaev magnet candidate BaCo2(AsO4)2

Candidate materials for the Kitaev spin liquid phase have been intensively studied recently because of their potential applications in fault-tolerant quantum computing. Although most of the studies on Kitaev spin liquid have been done in 4d- and 5d-based transition-metal compounds, recently there has been a growing research interest in Co-based quasi-two-dimensional honeycomb magnets, such as BaCo₂(AsO₄)₂ because of formation of spin-orbit-entangled J_eff = 1/2 pseudospin moments at Co²⁺ sites and potential realizations of Kitaev-like magnetism therein. Here, we obtain high-accuracy crystal and electronic structure of BaCo₂(AsO₄)₂ by employing combined density-functional and dynamical mean-field theory calculations, which correctly capture the Mott-insulating nature of the target system. We show that Co²⁺ ions form a high-spin configuration, S = 3/2, with an active L_eff = 1 orbital degree of freedom, in the absence of spin-orbit coupling. The size of trigonal distortion within CoO₆ octahedra is found to be not strong enough to completely quench the orbital degree of freedom, so that the presence of spin-orbit coupling can give rise to the formation of spin-orbit-entangled moments and the Kitaev exchange interaction. Our finding supports recent studies on potential Kitaev magnetism in this compound and other Co-based layered honeycomb systems.   

Electronic phase diagram of body-centered cubic structured alkali-doped fulleride

Motivated by the experimental phase diagram obtained by controlling the C$^{3-}_{60}$ molecular volume under the chemical pressure, we study the electronic phase diagram of body-centered cubic structured alkali-doped fulleride. In the presence of strong on-site interaction, first we convert the effective Hamiltonian into an exactly-solvable Hatsugai-Kohomoto-BCS type model. We find that the s-wave superconducting phase transition driven by the inverted Hund’s coupling term into non-Fermi liquid phase is a strongly first order one. Second, in the strongly correlated limit away from superconductivity, we use spin-rotation invariant slave boson approach to study the correlated electronic phases such as paramagnetic metallic phase, Mott insulating phase, and antiferromagnetic phase. Finaly, we construct the global phase diagram in temperature and C$^{3-}_{60}$ molecular volume parameter space.   

Comparing the electronic states of UGe2 and UTe2 using Relativistic Quantum Embedding

Abstract

We show that electronic states of UGe2 can be matched to those of UTe2 by scaling volume, motivating the formation of a unified phase diagram for the two materials. For example, the ambient pressure state of UGe2 resembles the state of a pressurized UTe2 . The unified phase diagram sheds new light on questions about the nature of itineracy / localization in these systems, the origin of magnetism, the role of symmetry and structure, crystal fields, and the role of correlations.

Our calculations are fully relativistic, charge-self-consistent DFT + many-body simulations, using Gutzwiller (RISB) and DMFT under the same Quantum Embedding framework (Portobello). Representation the off-diagonal Gutzwiller variables is necessary in order to capture the complementary spin-orbit coupling (SOC) and the anisotropic crystal fields, since they vary by comparable magnitudes of energy.

Finally we demonstrate how our the computational results agree with experimental observations.   

Multiboson exchange embedding for the Hubbard model

In condensed matter physics, strongly correlated electrons are paradigmatic examples of quantum many-body systems that defy a description in terms of simple band theory due to their strong interactions with each other and with the atomic lattice. Their study is both exciting and challenging, not only because the construction of accurate theoretical models requires the consideration of many different factors, such as spin, charge, and orbital degrees of freedom, but also because of the scarcity of exactly solvable reference Hamiltonians. For example, the single-band Hubbard model in more than one dimension has remained at the forefront of computational condensed matter physics for decades, although in many respects it can be regarded as the simplest incarnation of a reasonably realistic correlated electron system.

We present a novel quantum-embedding approach based on the single-boson exchange (SBE) decomposition of the parquet equations. In the SBE formalism, all diagrams contributing to the two-particle vertex F are grouped according to their interaction reducibility, i.e. the way in which they can be split into disconnected parts by removing a bare vertex. This way, unphysical divergences in two-particle irreducible quantities are efficiently mitigated and only the well-conditioned multiboson vertex M is needed to determine all other (single-boson and single-particle) functions self-consistently. Using the dynamical cluster approximation (DCA) with statistically exact CT-QMC simulations, we determine M for small Hubbard clusters coupled to a metallic environment and solve the self-consistent equations on periodic lattices with up to 24 x 24 sites, preserving the full frequency and momentum dependence of all single-boson exchange diagrams. We benchmark our approach against established many-body methods for the half-filled square lattice Hubbard model.   

Topological excitations and Postnikov data

Upon spontaneously breaking a continuous symmetry, the classical topological defects and textures of the resulting system are characterized by the homotopy groups of the resulting order parameter manifold. For example, in 2D magnetic systems with SO(3) symmetry spontaneously broken down to O(2), the order parameter manifold is two dimensional real projective space. The homotopy theory of this space implies that there is one species of vortex which is its own anti-vortex and that the textures of this system are skyrmions. Given the richness of mathematical theory of homotopy, one may wonder if it can tell us more than a basic zoology of excitations. In our work, we show that homotopy theory not only predicts the types of classical topological excitations, it also predicts how these excitations interact with one another. This information is contained in the so-called "Postnikov data." In this talk, we will show how "homotopy types" can be used to understand subtle information about classical topological excitations and its implications symmetry broken quantum topological order.   

Coarsening dynamics of charge density waves in Holstein-Hubbard model: Machine learning enabled large-scale dynamical simulations

We develop a machine learning (ML) force-field model to enable large-scale adiabatic dynamical simulations of the Holstein-Hubbard model on a square lattice. At small Hubbard repulsion, the system exhibits a robust charge density wave (CDW) order at half-filling. The adiabatic evolution of a CDW order is governed by the dynamics of the lattice distortion. Calculation of the electronic contribution to the driving forces, however, is computationally very expensive for large systems. Assuming the principle of locality for electron systems, a neural-network model is developed to accurately and efficiently predict local electronic forces with input from neighborhood configurations. Our large-scale thermal quench simulations uncover an anomalous growth of the CDW domains that deviates significantly from the expected Allen-Cahn law for phase ordering of Ising-type order parameter field. Moreover, we observe an intriguing non-monotonic dependence of CDW coarsening on the Hubbard repulsion, indicating nontrivial interplay between electron correlation and CDW dynamics.    

Voltage-controlled dynamics of metal-to-insulator phase transition in La0.67 Sr0.33MnO3 thin films exploiting negative differential resistance

Neuromorphic computing has gained ample interest due to energy-efficient solutions beyond the non-von Neumann approach, but at the hardware level, the present system lacks rich non-linear phenomenon that occurs in biological systems. An experimental realization of such a non-linear system requires tunable neuronal spiking, realized in Mott memristors that exhibit structural transition-induced electronic instabilities and manifest as a negative differential resistance (NDR). However, repeated structural transitions required to deliver such electronic instabilities hinder an efficient demonstration of spiking neural networks (SNN) due to internal strain build-up. Here we report on a new approach using the intrinsic metal-to-insulator coupled transition in La_0.67Sr_0.33MnO₃ without the requirement of a structural transition. Two distinct ‘S’ type NDR at different bias regimes have been observed on LSMO thin-film devices grown on textured LaAlO₃ substrate. Both bias regimes have been exploited to demonstrate voltage control oscillators with tunable frequencies. The textured substrate also provides anisotropic thermal interactions among multiple oscillatory devices, driving them either synchronously or asynchronously and is a crucial route towards stabilizing spiking neural networks.