Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session G49: Precision Many-Body Physics III: Modeling and Real MaterialsFocus Recordings Available
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Sponsoring Units: DCOMP DAMOP DCMP Chair: Javier Lopez, University of Massachusetts, Amherst Room: McCormick Place W-471B |
Tuesday, March 15, 2022 11:30AM - 12:06PM |
G49.00001: Variational wave functions for spin models with phonons and anisotropic-exchange couplings Invited Speaker: Federico Becca The definition of variational wave functions represents an invaluable tool to describe strongly-correlated systems. Examples are given by the Bardeen-Cooper-Schrieffer theory of superconductivity and the Laughlin's explanation of the fractional quantum Hall effect. A promising playground where this kind of approach has been fruitfully applied lies in highly-frustrated spin models, where the spin-liquid phases may emerge from the competition of various super-exchange interactions. These exotic states of matter are characterized by high entanglement, fractional excitations, and topological properties. Gutzwiller-projected wave functions (constructed from fermionic and bosonic constituents) have been employed since the pioneering suggestion by Anderson of the resonating-valence-bond theory. In the recent years, we demonstrated that the fermionic approach gives very accurate results in a wide range of SU(2) Heisenberg models on a wide variety of lattices (most importantly for the kagome lattice). The next challenge is now to incorporate further ingredients in the microscopic Hamiltonians, to get closer to actual materials. Examples are given by the inclusion of quantum phonons, the Dzyaloshinskii–Moriya interaction, and, more generally, anisotropic-exchange couplings (as present in Kitaev materials). Besides being relevant for an accurate description of real materials, these additional perturbations are extremely useful to assess the stability of spin-liquid phases, especially the gapless ones. In this talk, we discuss the accuracy of Gutzwiller-projected wave functions to determine the correct results of these extended models, focusing on the kagome lattice, which still continues to attract the attention of the community working on frustrated magnetism. |
Tuesday, March 15, 2022 12:06PM - 12:18PM |
G49.00002: Nevanlinna Analytical Continuation Emanuel C Gull, Jiani Fei Simulations of finite temperature quantum systems provide imaginary frequency Green's functions that correspond one-to-one to experimentally measurable real-frequency spectral functions. However, due to the bad conditioning of the continuation transform from imaginary to real frequencies, established methods tend to either wash out spectral features at high frequencies or produce spectral functions with unphysical negative parts. Here, we show that explicitly respecting the analytic 'Nevanlinna' structure of the Green's function leads to intrinsically positive and normalized spectral functions and we present a continued fraction expansion that yields all possible functions consistent with the analytic structure. Application to synthetic trial data shows that sharp, smooth, and multi-peak data is resolved accurately. Application to the band structure of silicon demonstrates that high energy features are resolved precisely. Continuations in a realistic correlated setup reveal additional features that were previously unresolved. By substantially increasing the resolution of the real frequency calculations, our work overcomes one of the main limitations of finite-temperature quantum simulations. |
Tuesday, March 15, 2022 12:18PM - 12:30PM |
G49.00003: Phase transitions in partial summation methods: Results from the 3D Hubbard model Sergei Iskakov, Emanuel C Gull The accurate determination of magnetic phase transitions in electronic systems is an important task of solid state theory. While numerically exact results are readily available for model systems such as the half-filled 3D Hubbard model, the complexity of real materials requires additional approximations, such as the restriction to certain classes of diagrams in perturbation theory, that reduce the precision with which magnetic properties are described. In this work, we examine the description of magnetic properties in second order perturbation theory, GW, FLEX, and two T-Matrix approximations to numerically exact CT-QMC reference data. We assess finite-size effects and compare periodic lattice simulations to cluster embedding. We find that embedding substantially improves finite size convergence. However, by analyzing different partial summation methods we find no systematic improvement in the description of magnetic properties, with most methods considered in this work predicting first-order instead of continuous transitions, leading us to the conclusion that non-perturbative methods are necessary for the accurate determination of magnetic properties and phase transitions. |
Tuesday, March 15, 2022 12:30PM - 12:42PM |
G49.00004: Benchmarking the TPSC+ Approach to the Two-Dimensional Hubbard Model Camille Lahaie, Chloé Gauvin-Ndiaye, A.-M. S Tremblay One of the important models for the study of electron interactions in strongly correlated materials is the Hubbard model. There is a handful of approaches to find approximate solutions to this model. One of these methods is the Two-Particle Self-Consistent approach (TSPC) [1], which satisfies a number of exact results and which has been used to study electron-doped cuprates successfully. However, this method is not valid in regimes where the antiferromagnetic correlation length becomes too large. |
Tuesday, March 15, 2022 12:42PM - 12:54PM |
G49.00005: Benchmark of the TPSC+DMFT approach for the Hubbard model Nicolas B Martin, Chloé Gauvin-Ndiaye, A.-M. S Tremblay The two-particle self-consistent approach (TPSC) is an effective tool for studying systems that can be modelled by a single-band Hubbard model at weak to intermediate coupling strength [1, 2]. However, the results obtained by this method on a 2D square lattice are poor in the renormalized classical regime. We show how using double-occupancy and self-energy results from single-site dynamical mean field theory (DMFT) can improve this approach, while removing the need for the TPSC ansatz. In this work, we apply the proposed method to a 2D square lattice with nearest-neighbor hopping. We benchmark our approach using Monte-Carlo results [2] for the magnetic correlation length and the self-energy. |
Tuesday, March 15, 2022 12:54PM - 1:06PM |
G49.00006: Diagrammatic quantum Monte Carlo study of an acoustic lattice polaron Thomas Hahn, Cesare Franchini, Naoto Nagaosa, Andrey Mishchenko We present a diagrammatic Monte Carlo study of a lattice polaron interacting with an acoustic phonon branch through the deformation potential. Weak and strong coupling regimes are separated by a self-trapping region where quantum resonance between various possible lattice deformations is seen in the ground-state properties, spectral function, and optical conductivity. This study shows that the acoustic lattice polaron represents a distinct quantum object with unique features, markedly different from any previously considered polaron model. In particular, the acoustic lattice polaron exhibits an interplay between long- and short wavelength acoustic vibrations, resulting in a composite phonon cloud which leads to the formation of multiple competing polaron states with a complex spectral response. |
Tuesday, March 15, 2022 1:06PM - 1:18PM |
G49.00007: Optical Conductivity of the Two Dimensional Hubbard Model: Exact Perturbative vs Dynamical Mean Field Results Anqi Mu, Zhiyuan Sun, Andrew J Millis We compute the frequency dependent conductivity including the total spectral weight and Drude weight of the two dimensional square lattice Hubbard model at zero temperature as a function of density in the weak interaction limit using both exact perturbation and the dynamical mean field approximation. We find that dynamical mean field approximation, which ignores the vertex correction, fails to capture the correct low frequency behavior of the optical conductivity for low band filling when there is approximate Galilean invariance, and around half filling when nesting effect is important. |
Tuesday, March 15, 2022 1:18PM - 1:30PM |
G49.00008: Real-frequency responses at finite temperature: Electron gas Igor Tupitsyn, Alexei M Tsvelik, Robert M Konik, Nikolay Prokofiev To connect finite-temperature calculations with experimental probes not based on thermodynamic potentials, one needs to compute response functions (or spectral densities) at real frequencies. The notorious problem faced by simulations performed in the Matsubara representation is a need for a numerical analytic continuation (NAC) procedure from the imaginary to the real-frequency domain because even if the Matsubara data are known with high accuracy, the NAC will fail to correctly reproduce complex spectra. Here we show that the Diagrammatic Monte Carlo technique allows one to compute finite-temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system's action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. The feasibility of the method is demonstrated by considering the problem of the plasmon line-width in a homogeneous electron gas. |
Tuesday, March 15, 2022 1:30PM - 1:42PM |
G49.00009: On the closedness and geometry of tensor network state sets Thomas Barthel, Jianfeng Lu, Gero Friesecke Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. We discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states (TTNS), and the multiscale entanglement renormalization ansatz (MERA) are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states (PEPS) are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof. |
Tuesday, March 15, 2022 1:42PM - 1:54PM |
G49.00010: Properties of the isothermal compressibility in the 2D t-J model William O Putikka The isothermal compressibility for the 2D t-J model has been calculated for the full range of densities at J/t = 0.4 by using a 12th order high temperature expansion. The compressibility is found to have a subtantial peak for n ≈ 0.8, where the dominant fluctuations in the model change from antiferromagnetic fluctuations for n ≥ 0.8 to d-wave pair fluctuations for n ≤ 0.8. A smaller peak is found near n ≈ 0.5. For densities below this smaller peak it is likely d-wave pair fluctuations are no longer present. Results from the temperature derivative of the pressure and the d-wave pair correlation length show changes in behavior where the compressibility has peaks. |
Tuesday, March 15, 2022 1:54PM - 2:06PM |
G49.00011: A hydrogenic chain in a non-orthogonal basis: Beyond the Hubbard model Samuel J Milner, Philip Weinberg, Adrian E Feiguin The Hubbard model was first proposed in a paper by J. Hubbard in 1963 to describe strong interactions between fermions on a lattice. We have extended these ideas by including the effects of overlaps between adjacent orbitals on a hydrogenic chain of atoms in a spirit similar to the derivation of the Pariser-Parr-Popple (PPP) model. As a consequence, the Schrödinger equation becomes a generalized eigenvalue problem. We orthogonalize the basis using a Löwdin transformation, resulting in a Hamiltonian with long-range hopping and interactions in real space that also breaks particle-hole symmetry. We study the implications on the metal-insulator transition in 1D and calculate spectral functions with the density matrix renormalization group (DMRG) method. |
Tuesday, March 15, 2022 2:06PM - 2:18PM |
G49.00012: 1D-to-3D crossover on multileg attractive-U Hubbard ladders Ian Pilé, Anastasia Potapova, Evgeni Burovski We study ground state properties of a polarized two-component Fermi gas on multileg attractive-U Hubbard ladders. Using DMRG simulations, we construct grand canonical phase diagrams for varying perpendicular geometries and ratios of hopping amplitudes, and charactrize the 1D-to-3D crossover. We compare our findings with recent experiemental and theoretical studies of quasi-one-dimensional polarized Fermi gases. |
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