Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session K48: Quantum Many-Body Systems and Methods IIRecordings Available
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Sponsoring Units: DCOMP Chair: Alina Kononov, Sandia National Lab Room: McCormick Place W-471A |
Tuesday, March 15, 2022 3:00PM - 3:12PM |
K48.00001: Quantification of electron correlation for approximate quantum calculations. Shunyue Yuan, Lucas K Wagner Many-body quantum systems are often divided into “strongly correlated” and “weakly correlated.” In strongly correlated systems, the determinant expansion of eigenstates includes several determinants with large weights, while in weakly correlated systems, the expansion is instead dominated by a single determinant. What sort of correlation is present can strongly affect the efficiency of a given approximate wave function method. For example, according to lore in the field, selected configuration interaction methods are efficient when there are just a few determinants with large weights. On the contrary, Slater-Jastrow wave functions are efficient for weakly correlated systems. |
Tuesday, March 15, 2022 3:12PM - 3:24PM |
K48.00002: A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities. Haihan Zhou, Anthony Scemama, Guangming Wang, Abdulgani Annaberdiyev, Benjamin E Kincaid, Michel Caffarel, Lubos Mitas We consider the real-space, fixed-node diffusion Monte Carlo (DMC) method that involves Hamiltonians with nonlocal operators, which could break the fixed-node constraint, and therefore proper algorithmic adjustments are necessary, for example, localization approximation. |
Tuesday, March 15, 2022 3:24PM - 3:36PM |
K48.00003: Auxiliary boson diffusion Monte Carlo approach for excitations Fernando A Reboredo, Jaron T Krogel A theoretical method to evaluate the excitation spectra of an interacting system from the ground state of an auxiliary system is presented and tested in a model system. The imaginary time evolution of an arbitrary state can be obtained by sampling the ground state distribution of walkers, and the gradients of the distribution of walkers of an auxiliary bosonic system. The wave-function of each excitation is expanded into a product of bosonic and fermionic wavefunctions. The bosonic function is treated statistically in DMC while the fermionic part is expanded in a basis and evaluated numerically. A fermion-boson coupling term appears that can be sampled on the bosonic ground state. The bosonic factor is expected to reduce the size of the basis required by the fermionic component: we show it incorporates in DMC the correlations missed by standard Jastrow factors. The implementation of this method in current DMC codes will be facilitated by reuse of procedures already developed and tested for the calculation of ground state properties with DMC or excitations with variational Monte Carlo(VMC). The perspectives and potential problems of this method when applied to realistic fermionic systems are discussed. |
Tuesday, March 15, 2022 3:36PM - 3:48PM |
K48.00004: Combining branching random walks with Metropolis sampling: constraint release in auxiliary-field quantum Monte Carlo Zhi-Yu Xiao We present an approach to combine the branching random walks of auxiliary-field quantum Monte Carlo (AFQMC) with Markov chain Monte Carlo sampling. The formulation of branching random walks along imaginary-time is required to realize a constraint on the paths to control the sign or phase problem, according to an exact gauge condition which, in practice, is implemented approximately with a trial wave function or trial density matrix. We use the generalized Metropolis algorithm to sample a selected portion of the imaginary-time path after it has been produced by the branching random walk. This allows a constraint release to follow seamlessly from the constrained-path sampling, which can reduce the systematic error from the latter. It also provides a way to improve the computation of correlation functions and observables which do not commute with the Hamiltonian. We illustrate the method in a number of atoms/molecules, where improvements in accuracy are observed and near-exact results are obtained. |
Tuesday, March 15, 2022 3:48PM - 4:00PM |
K48.00005: Electronic temperature effects on the dissociation of diatomic molecules using density matrix quantum Monte Carlo Hayley R Petras, William Z Van Benschoten, Emily J Landgreen, Sai Kumar Ramadugu, James J Shepherd We present data from finite temperature calculations on dissociation curves from density matrix quantum Monte Carlo methods. We describe how strong correlation changes in the diatomics as a function of temperature through an analysis of the population distribution on the density matrix for various bond lengths and the isolated atoms. This is then related to selected applications in surface chemistry. |
Tuesday, March 15, 2022 4:00PM - 4:12PM |
K48.00006: Decomposed Functional Renormalization Group Flows for Multi-band Hamiltonians Nahom K Yirga, David K Campbell We use a singular value decomposition to decouple the functional Renormalization group (fRG) equations in the |
Tuesday, March 15, 2022 4:12PM - 4:24PM |
K48.00007: Multi-Method, Multi-Messenger Approaches to Models of Strong Correlations Thomas Schaefer, Nils Wentzell, Fedor Simkovic, Yuan-Yao He, Marcel Klett, Christian J Eckhardt, Behnam Arzhang, Viktor Harkov, Aaram J Kim, Evgeny Kozik, Evgeny A Stepanov, Anna Kauch, Sabine Andergassen, Philipp Hansmann, Daniel Rohe, James LeBlanc, Shiwei Zhang, A.-M. S Tremblay, Michel Ferrero, Olivier P Parcollet, Alexander Wietek, Riccardo Rossi, Miles Stoudenmire, Antoine Georges The Hubbard model is the paradigmatic model for electronic correlations. In this talk I present a general framework for the reliable calculation of its properties, which we coined 'multi-method, multi-messenger' approach. I will illustrate the power of this approach with two recent studies: (i) an extensive synopsis of arguably all available finite-temperature methods for the half-filled Hubbard model on a simple square lattice in its weak-coupling regime and (ii) a complementary subset of those applied to the Hubbard model on a triangular geometry. While the former example fully clarifies the impact of spin fluctuations and tracks it footprints on the one- and two-particle level, the latter exhibits the intriguing interplay of geometric frustration (magnetism) and strong correlations (Mottness). These examples may work as a blueprint for similar future studies of strongly correlated systems. |
Tuesday, March 15, 2022 4:24PM - 4:36PM |
K48.00008: Fluctuation Approach to Many-Body Quantum Dynamics Erik Schroedter, Jan-Philip Joost, Michael Bonitz The dynamics of quantum many-body systems following external excitation is of great interest in many areas such as dense plasmas or correlated solids. At present, only the formalism of nonequilibrium Green functions (NEGF) can rigorously describe such processes in more than one dimension. However, NEGF simulations are computationally expensive, among other things, due to their cubic scaling with simulation time T. Only recently, linear scaling with T could be achieved within the G1-G2 scheme [1]. Here a new fluctuation based approach to the NEGF formalism is presented. While in theory the resulting equations are fully equivalent to the G1-G2 scheme, in practice the new approach has interesting complementary features such as the capability to simulate many-body effects using stochastic methods [2], which further reduce the computational complexity and increase numerical stability for stronger coupling. Additionally, this approach provides direct access to spectral two-particle quantities such as the density response function or polarizability. |
Tuesday, March 15, 2022 4:36PM - 4:48PM |
K48.00009: Electron-phonon excitations in the 1D Hubbard-Holstein model probed by Resonant Inelastic X-Ray Scattering Jinu Thomas, Alberto Nocera, Steven S Johnston The prospect of accessing electron-phonon (e-p) coupling strengths using resonant inelastic x-ray scattering (RIXS) has attracted significant attention in recent years. With current energy resolution, RIXS experiments can now resolve individual phonon modes. Standard analysis for such experiments is done by using a single site Lang Firsov (LF) model that promises to extract quantative information on momentum resolved e-p coupling by fitting data. This method, however, computes the phonon RIXS intensities by approximating the electron-phonon interaction in the atomic limit, coupling a single electronic excitation to a single phonon mode. It remains unclear if such a drastic approximation remains valid for a many-particle system with itinerant carriers. We test the validity of this model in the strongly correlated many-particle limit. By explicitly computing the RIXS intensity using DMRG, we study the phonon excitations in finite-sized Hubbard-Holstein chains and compare our results against the single-site and the single-band predictions. |
Tuesday, March 15, 2022 4:48PM - 5:00PM |
K48.00010: Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model at Finite Temperature Bo Xiao, Yuan-Yao He, Shiwei Zhang Competing orders, including inhomogeneous spin and charge orders, are observed in many correlated electron materials, including the high-temperature superconductors. The two-dimensional Hubbard model provides a minimal paradigm for studying these orders. Using constrained-path auxiliary-field quantum Monte Carlo, We study the interplay between thermal and quantum fluctuations in this model. Reaching large supercell sizes to extract properties in the thermodynamics limit, we obtain an accurate and systematic characterization of the behaviors of the spin and charge orders as a function of temperature. In all three electron densities, we find increasing short-range antiferromagnetic correlations as temperature is lowered. As the correlation length grows sufficiently large, a modulating wave appears to produce spin-density-wave (SDW). In the case of ρ=0.9 and 0.875, this evolves smoothly into the ground-state long-range SDW order. In the case of ρ=0.8, the SDW remains short-ranged as temperature is lowered to zero. We study the interplay between spin and charge orders and find that formation of charge order appears to follow that of spin order. This leads to a very low upper bound for the transition temperature for CDW or stripe order. |
Tuesday, March 15, 2022 5:00PM - 5:12PM |
K48.00011: A new Time-Domain Approach for Linear Responses and Charge Transport Michel Panhans Linear-response theory is a powerful theoretical framework to investigate, e.g., electrical and magnetic transport and to compare |
Tuesday, March 15, 2022 5:12PM - 5:24PM |
K48.00012: Effects of operator backflow on quantum transport Tibor Rakovszky, Curt von Keyserlingk, Frank Pollmann Tensor product states have proved extremely powerful for simulating the low-temperature properties of many-body systems. The applicability of such methods to the dynamics of many-body systems is less clear: as entanglement grows under time evolution, memory requirements or truncation errors spiral out of control. In this talk, we present a method that seeks to reduce this memory barrier by selectively discarding highly non-local correlations in a controlled manner. We illustrate our method on various model systems and develop a theory to estimate the size of the error from the neglected "backflow" processes from nonlocal to local quantities. Our results suggest that backflow errors are exponentially suppressed in the size-cutoff; based on this result, we conjecture that the numerical resources needed to capture transport coefficients in ergodic diffusive systems scale effectively polynomially with the required precision, significantly better than the exponential scaling of more brute-force methods. We also discuss how our method performs compared to other approximation schemes. |
Tuesday, March 15, 2022 5:24PM - 5:36PM |
K48.00013: Direct solution of multiple excitations in a matrix product state with block Lanczos David Sénéchal, Alexandre Foley, Thomas E Baker Matrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one dimension. We introduce the multi-targeted method that acts on a bundled matrix product state, holding many excitations. The use of a block or banded Lanczos algorithm allows for the simultaneous, variational optimization of the bundle of excitations. The method is demonstrated on a Heisenberg model and other cases of interest. A large of number of excitations can be obtained at a small bond dimension with highly reliable local observables throughout the chain. |
Tuesday, March 15, 2022 5:36PM - 5:48PM |
K48.00014: Relativistic three-boson bound states in the zero-range limit Mohammadreza Hadizadeh, Kamyar Mohseni, Andre J Chaves, Diego Rabelo da Costa, Tobias Frederico The relativistic Faddeev integral equations are solved to calculate three-boson mass and wave function for ground and excited states. The inputs of relativistic Faddeev integral equations are the fully-off-shell boosted t-matrices, calculated from the boosted interactions by solving the relativistic Lippmann-Schwinger equation. We employ Kamada and Glöcke boosted potentials obtained directly from nonrelativistic short-range separable potentials by solving a quadratic integral equation using an iterative scheme. By adopting Yamaguchi and Gaussian potentials and driving them towards the zero-range limit, we show that relativistic masses and wave functions are model-independent, and the Thomas collapse is avoided, while the nonrelativistic limit keeps the Efimov effect. We compare our results for relativistic masses with Light-Front and Euclidean calculations. |
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