A Stable, Recursive Auxiliary Field Quantum Monte Carlo Algorithm in the Canonical Ensemble: Applications to Thermometry and the Hubbard Model

Abstract

Many experimentally-accessible, finite-sized interacting quantum systems are most appropriately described by the canonical ensemble of statistical mechanics. Conventional numerical simulation methods either approximate them as being coupled to a particle bath, or use projective algorithms which may suffer from non-optimal scaling with system size or large algorithmic prefactors. In this paper, we introduce a highly stable, recursive Auxiliary Field Quantum Monte Carlo approach that can directly simulate systems in the canonical ensemble. We apply the method to the fermion Hubbard model in one and two spatial dimensions in a regime known to exhibit a significant "sign" problem and find improved performance over existing approaches including rapid convergence to ground state expectation values. The effects of excitations above the ground state are quantified using an estimator-agnostic approach including studying the temperature dependence of the purity and overlap fidelity of the canonical and grand canonical density matrices. As an important application, we show that thermometry approaches often exploited in ultra-cold atoms that employ an analysis of the velocity distribution in the grand canonical ensemble may be subject to errors leading to an under-estimation of extracted temperatures with respect to the Fermi temperature.

arXiv comment14 pages, 7 figures, and Supplemental Information with key derivations. For associated data and code repository see: https://github.com/DelMaestroGroup/papers-code-CanEnsAFQMC

References in corpus (51)

• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Probing many-body states of ultra-cold atoms via noise correlations
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Spin and Charge Resolved Quantum Gas Microscopy of Antiferromagnetic Order in Hubbard Chains
• A Constrained Path Monte Carlo Method for Fermion Ground States
• The entanglement of indistinguishable particles shared between two parties
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• Nuclear Level Density and the Determination of Thermonuclear Rates for Astrophysics
• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• Homogeneous Atomic Fermi Gases
• Monte Carlo evaluation of path integrals for the nuclear shell model
• Universal behavior of pair correlations in a strongly interacting Fermi gas
• Quantum Gases in Optical Boxes
• Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
• Two-Dimensional Homogeneous Fermi Gases
• \textit{Ab Initio} Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter
• Total and Parity-Projected Level Densities of Iron-Region Nuclei in the Auxiliary Fields Monte Carlo Shell Model
• Coupled cluster theory in materials science
• Rényi generalization of the operational entanglement entropy
• Accurate exchange-correlation energies for the warm dense electron gas
• Entanglement constrained by superselection rules
• Cooling and thermometry of atomic Fermi gases
• An alternative quantum fidelity for mixed states of qudits
• Path Integral Molecular Dynamics for Bosons
• Interaction Picture Density Matrix Quantum Monte Carlo
• Demonstration of the auxiliary-field Monte Carlo approach for sd-shell nuclei
• Finite-Temperature Monte Carlo Calculations For Systems With Fermions
• Heavy deformed nuclei in the shell model Monte Carlo method
• Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
• Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo
• Calculation of thermodynamic properties of finite Bose-Einstein systems
• Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
• Measurement of the Dynamical Structure Factor of a 1D Interacting Fermi Gas
• Finite-Temperature Auxiliary-Field Quantum Monte Carlo for Bose-Fermi Mixtures
• Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble
• Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble
• Pairing correlations across the superfluid phase transition in the unitary Fermi gas
• Finite-temperature many-body perturbation theory in the grand canonical ensemble
• Thermodynamic fermion-boson symmetry in harmonic oscillator potentials
• Finite-size effects in canonical and grand-canonical quantum Monte Carlo simulations for fermions
• Quantum Monte Carlo measurement of the chemical potential of helium-4
• Pair condensation in a Finite Trapped Fermi Gas
• Unveiling the Finite Temperature Physics of Hydrogen Chains via Auxiliary Field Quantum Monte Carlo
• Dynamical tuning of the chemical potential to achieve a target particle number in grand canonical Monte Carlo simulations
• Deviations from Wick's theorem in the canonical ensemble
• Stabilizing Canonical-Ensemble Calculations in the Auxiliary-Field Monte Carlo Method
• An entropy perspective on the thermal crossover in a fermionic Hubbard chain
• Correlations of occupation numbers in the canonical ensemble and application to BEC in a 1D harmonic trap
• Canonical and Grand Canonical Ensemble Expectation Values from Quantum Monte Carlo Simulations

Cited by in corpus (6)

• Quadratic Scaling Bosonic Path Integral Molecular Dynamics
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• Disentangling the Physics of the Attractive Hubbard Model via the Accessible and Symmetry-Resolved Entanglement Entropies
• Exact kinetic propagators for coherent state complex Langevin simulations
• A projected complex Langevin sampling method for bosons in the canonical and microcanonical ensembles
• Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice