Quantum Many-Body Calculations using Body-Centered Cubic Lattices

Abstract

It is often computationally advantageous to model space as a discrete set of points forming a lattice grid. This technique is particularly useful for computationally difficult problems such as quantum many-body systems. For reasons of simplicity and familiarity, nearly all quantum many-body calculations have been performed on simple cubic lattices. Since the removal of lattice artifacts is often an important concern, it would be useful to perform calculations using more than one lattice geometry. In this work we show how to perform quantum many-body calculations using auxiliary-field Monte Carlo simulations on a three-dimensional body-centered cubic (BCC) lattice. As a benchmark test we compute the ground state energy of 33 spin-up and 33 spin-down fermions in the unitary limit, which is an idealized limit where the interaction range is zero and scattering length is infinite. As a fraction of the free Fermi gas energy $E_{\mathrm{FG}}$, we find that the ground state energy is $E_0/E_{\mathrm{FG}}=0.369(2),0.371(2),$ using two different definitions of the finite-system energy ratio. This is in excellent agreement with recent results obtained on a cubic lattice \cite{He:2019ipt}. We find that the computational effort and performance on a BCC lattice is approximately the same as that for a cubic lattice with the same number of lattice points. We discuss how the lattice simulations with different geometries can be used to constrain the size lattice artifacts in simulations of continuum quantum many-body systems.

13 pages, 7 figures

References in corpus (22)

• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Thermodynamics of the BCS-BEC crossover
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Epsilon expansion for a Fermi gas at infinite scattering length
• Quantum Monte Carlo Simulations of the BCS-BEC Crossover at Finite Temperature
• The potential energy of a ${}^{40}$K Fermi gas in the BCS-BEC crossover
• Thermodynamic Measurements in a Strongly Interacting Fermi Gas
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Large-N expansion for unitary superfluid Fermi gases
• Resonantly Interacting Fermions In a Box
• BEC-BCS crossover and universal relations in unitary Fermi gases
• Momentum Distribution and Contact of the Unitary Fermi gas
• The ground state energy at unitarity
• Density-functional theory for fermions in the unitary regime
• Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length
• Two-particle scattering on the lattice: Phase shifts, spin-orbit coupling, and mixing angles
• Sign-free stochastic mean-field approach to strongly correlated phases of ultracold fermions
• Precision benchmark calculations for four particles at unitarity
• Ground-state energy of the unitary Fermi gas from the epsilon expansion
• Neutrino scattering in supernovae and spin correlations of a unitary gas
• Sampling General N-Body Interactions with Auxiliary Fields

Cited by in corpus (1)

• Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations