Gauge auxiliary-field quantum Monte Carlo method for many-fermion systems

Hao Shi, Yuan-Yao He, Shiwei Zhang

W. K. Kellogg Radiation Laboratory

Zhaozhan Zhang

We propose novel Quantum Monte Carlo (QMC) methods for interacting many-fermion systems by leveraging the stochastic gauge freedom, originally developed in Gaussian phase-space QMC, within the phaseless auxiliary-field QMC (AFQMC) framework. In particular, we reinterpret the conventional force bias in phaseless AFQMC as a drift gauge and explore Fermi gauges based on natural orbitals of a reduced one-body density matrix defined via a mixed estimator, yielding stochastic, time-dependent Hartree-Fock-like dynamics. We propose a symmetry-projection sampling scheme to enhance the sampling efficiency. As a proof of concept, we apply these gauge-augmented AFQMC methods to a simple shell-model Hamiltonian: the Lipkin-Meshkov-Glick model. Numerical results illustrate the potential of stochastic gauges to enhance accuracy and reduce fluctuations, underscoring the promise for advancing these new techniques toward more realistic shell-model applications.

Gayle A. Sugiyama, S. E. Koonin

Brenda M. Rubenstein, Shiwei Zhang, David R. Reichman

We present a quantum Monte Carlo (QMC) technique for calculating the exact finite-temperature properties of Bose-Fermi mixtures. The Bose-Fermi auxiliary-field quantum Monte Carlo (BFAFQMC) algorithm combines two methods, a finite-temperature AFQMC algorithm for bosons and a variant of the standard AFQMC algorithm for fermions, into one algorithm for mixtures. We demonstrate the accuracy of our method by comparing its results for the Bose-Hubbard and Bose-Fermi-Hubbard models against those produced using exact diagonalization for small systems. Comparisons are also made with mean-field theory and the worm algorithm for larger systems. As is the case with most fermion Hamiltonians, a sign or phase problem is present in the BFAFQMC algorithm. We discuss the nature of these problems in this framework and describe how they can be controlled with well-studied approximations to expand the BFAFQMC algorithm's reach. This algorithm can serve as an essential tool for answering many unresolved questions about many-body physics in mixed Bose-Fermi systems.

M. Motta, Davide Emilio Galli, S. Moroni +1 more

The phaseless Auxiliary Field Quantum Monte Carlo (AFQMC) method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we address the possibility of calculating imaginary time correlation functions with the phaseless AFQMC. We give a detailed description of the technique and test the quality of the results for static properties and imaginary time correlation functions against exact values for small systems.