Auxiliary Field quantum Monte Carlo for Strongly Paired Fermions

Abstract

We demonstrate that the inclusion of a BCS importance function dramatically increases the efficiency of the auxiliary field method for strong pairing. We calculate the ground-state energy of an unpolarized fermi gas at unitarity with up to 66 particles and lattices of up to $27^3$ sites. The method has no fermion sign problem, and an accurate result is obtained for the universal parameter $\xi$. Several different forms of the kinetic energy adjusted to the unitary limit but with different effective ranges extrapolate to the same continuum limit within error bars. The finite effective range results for different interactions are consistent with a linear term proportional to the Fermi momentum times the effective range. The new method described herein will have many applications in superfluid cold atom systems and in both electronic and nuclear structures when pairing is important.

5 pages, 2 figures

References in corpus (10)

• Collective excitations of a degenerate gas at the BEC-BCS crossover
• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Thermodynamic Measurements in a Strongly Interacting Fermi Gas
• Resonantly Interacting Fermions In a Box
• Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
• BEC-BCS crossover and universal relations in unitary Fermi gases
• The ground state energy at unitarity
• Pair correlations of an expanding superfluid Fermi gas
• Precision benchmark calculations for four particles at unitarity
• Superfluidity and excitations at unitarity

Cited by in corpus (113)

• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
• Neutron Matter from Low to High Density
• The equation of state of neutron matter, symmetry energy, and neutron star structure
• Precise determination of the structure factor and contact in a unitary Fermi gas
• Linear Response on a Quantum Computer
• Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
• Exact Numerical Results on the Ground State of Strongly Interacting Fermi Gases in Two Dimensions
• The critical velocity in the BEC-BCS crossover
• Symmetry in Auxiliary-Field Quantum Monte Carlo Calculations
• Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases
• Quantized Superfluid Vortex Rings in the Unitary Fermi Gas
• Time-Dependent Density Functional Theory and the Real-Time Dynamics of Fermi Superfluids
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Quantum Monte Carlo approaches to nuclear and atomic physics
• Some Recent Developments in Auxiliary-Field Quantum Monte Carlo for Real Materials
• Effective-Range Dependence of Resonantly Interacting Fermions
• Lattice methods for strongly interacting many-body systems
• Lattice Monte Carlo calculations for unitary fermions in a finite box
• Pseudogaps in strongly interacting Fermi gases
• Ab initio nuclear thermodynamics
• The Equation of State of the Unitary Fermi Gas: An Update on Lattice Calculations
• Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases
• Time-Dependent Density Functional Theory for Fermionic Superfluids: from Cold Atomic Gases, to Nuclei and Neutron Stars Crust
• Perturbative quantum Monte Carlo method for nuclear physics
• Neutron stars and the dense matter equation of state: from microscopic theory to macroscopic observations
• First and second sound in a highly elongated Fermi gas at unitarity
• The contact in the unitary Fermi gas across the superfluid phase transition
• Critical temperature and superfluid gap of the Unitary Fermi Gas from Functional Renormalization
• Quantum Monte Carlo with Coupled-Cluster wave functions
• Pairing correlations across the superfluid phase transition in the unitary Fermi gas
• Emergence of a pseudogap in the BCS-BEC crossover
• The temperature evolution of the shear viscosity in a unitary Fermi gas
• Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space
• Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
• Universality of the unitary Fermi gas: A few-body perspective
• Dynamic density and spin responses of a superfluid Fermi gas in the BCS-BEC crossover: Path integral formulation and pair fluctuation theory
• The ${}^1$S${}_0$ pairing gap in neutron matter
• CPMC-Lab: A Matlab Package for Constrained Path Monte Carlo Calculations
• Fermionic shock waves - dissipative or dispersive?
• From resonantly interacting fermions with effective range to neutron matter
• Predicting Energies of Small Clusters from the Inhomogeneous Unitary Fermi Gas
• The pseudogap regime in the unitary Fermi gas
• Auxiliary-field based trial wave functions in quantum Monte Carlo calculations
• Stoner ferromagnetism of a strongly interacting Fermi gas in the quasirepulsive regime
• Towards Quantum Turbulence in Cold Atomic Fermionic Superfluids
• Rashba spin-orbit coupling, strong interactions, and the BCS-BEC crossover in the ground state of the two-dimensional Fermi Gas
• Effective-range dependence of resonant Fermi gases
• Auxiliary Field Quantum Monte Carlo for Multiband Hubbard Models: Controlling the Sign and Phase Problems to Capture Hund's Physics
• Eliminating the wave function singularity for ultracold atoms by similarity transformation
• Finite-range effects in the unitary Fermi polaron
• Reentrant BCS-BEC crossover and a superfluid-insulator transition in optical lattices
• Improved lattice operators for non-relativistic fermions
• BCS-BEC crossover of atomic Fermi superfluid in a spherical bubble trap
• Effective field theory for dilute Fermi systems at fourth order
• Contact interaction in an unitary ultracold Fermi gas
• Precision Many-Body Study of the Berezinskii-Kosterlitz-Thouless Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas
• Calculating ground state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches
• Neural Wave Functions for Superfluids
• Precursor of Superfluidity in a Strongly Interacting Fermi Gas with Negative Effective Range
• Ab Initio Electronic Structure Calculations by Auxiliary-Field Quantum Monte Carlo
• Superfluid Condensate Fraction and Pairing Wave Function of the Unitary Fermi Gas
• Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems
• Lattice approaches to dilute Fermi gases: Legacy of broken Galilean invariance
• Stabilizing Canonical-Ensemble Calculations in the Auxiliary-Field Monte Carlo Method
• Zero-temperature phase diagram of Yukawa bosons
• Lattice theory for nonrelativistic fermions in one spatial dimension
• Normal mass density of a superfluid Fermi gas at unitarity
• Fermionic Quantum Turbulence: Pushing the Limits of High-Performance Computing
• Signatures of the BCS-BEC crossover in the yrast spectra of Fermi quantum rings
• Theory of strongly paired fermions with arbitrary short-range interactions
• The Operator Product Expansion Beyond Leading Order for Two-Component Fermions
• Vortex line in the unitary Fermi gas
• Machine-learning approach to finite-size effects in systems with strongly interacting fermions
• A Pseudo-BCS Wavefunction from Density Matrix Decomposition:Application in Auxiliary-Field Quantum Monte Carlo
• Tensor-force effects on nuclear matter in relativistic ab initio theory
• Effect of the particle-hole channel on BCS--Bose-Einstein condensation crossover in atomic Fermi gases
• Small two-component Fermi gases in a cubic box with periodic boundary conditions
• From weak to strong: constrained extrapolation of perturbation series with applications to dilute Fermi systems
• Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method
• Dynamic structure factor of a strongly correlated Fermi superfluid within a density functional theory approach
• Thermodynamic equivalence of two-dimensional imperfect attractive Fermi and repulsive Bose gases
• Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications
• Transdimensional equivalence of universal constants for Fermi gases at unitarity
• Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content
• FFLO order in ultra-cold atoms in three-dimensional optical lattices
• Detecting Entrainment in Fermi-Bose Mixtures
• Sensitivity to the initial conditions of the Time-Dependent Density Functional Theory
• Quantum Many-Body Calculations using Body-Centered Cubic Lattices
• Are smooth pseudopotentials a good choice for representing short-range interactions?
• Quantum Monte Carlo study of strongly interacting Fermi gases
• Mean-field vs RPA calculation of the energy of an impurity immersed in a spin 1/2 superfluid
• Low-momentum interactions for ultracold Fermi gases
• Lattice Improvement in Lattice Effective Field Theory
• Implementing advanced trial wave functions in fermion quantum Monte Carlo via stochastic sampling
• Response functions for the two-dimensional ultracold Fermi gas: dynamical BCS theory and beyond
• Auxiliary Field Quantum Monte Carlo for Dilute Neutrons on the Lattice
• Three-body contact for fermions. I. General relations
• Numerical study of unitary fermions in one spatial dimension
• Observation of collectivity enhanced magnetoassociation of ${}^6$Li in the quantum degenerate regime
• Constrained extrapolation problem and order-dependent mappings
• Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree-Fock-Bogoliubov wavefunctions
• NNQS-AFQMC: Neural network quantum states enhanced fermionic quantum Monte Carlo
• Cold atoms beyond atomic physics
• BCS-BEC crossover of the strongly interacting ${}^6$Li-${}^{40}$K mixture
• Accelerating ground-state auxiliary-field quantum Monte Carlo simulations by delayed update and block force-bias update
• Exact evaluation of large-charge correlation functions in non-relativistic conformal field theory
• An Effective Series Expansion to the Equation of State of Unitary Fermi Gases
• The normal state of attractive Fermi gases from coupled-cluster theory
• Proton fraction in neutron star matter: Dynamical mean-field approach
• Ab initio study of the neutron and Fermi polarons on the lattice