Finite-temperature auxiliary-field quantum Monte Carlo for Bose-Fermi mixtures

Brenda Rubenstein, Columbia University

Rapid advances in ultracold atomic physics have paved the way toward experimentally emulating many of the fundamental models of condensed matter physics with fine control for the very first time. Past success emulating the superfluid-Mott insulator transition in Bose gases and Fermi pressure in Fermi gases has stimulated interest in Bose-Fermi mixtures. Analytical work suggests that Bose-Fermi mixtures possess a rich phase diagram, yet many of the phase diagram’s most interesting features are beyond the reach of current computational techniques, which are limited to one-dimensional explorations. In this work, we outline how Bose-Fermi mixtures may be studied free of the sign and phase problems using finite-temperature auxiliary-field quantum Monte Carlo with the phaseless and constrained-path approximations. One of our key results is the derivation of a single-particle bosonic Green’s function, which enables simulation of bosonic systems in any number of dimensions, at any physical value of the temperature and chemical potential. We benchmark our Monte Carlo results against exact results for multidimensional bosonic systems and furthermore demonstrate the novelty of our method by studying the onset of collapse in correlated Bose-Fermi mixtures. We use our method to obtain the exact superfluid-Mott insulator phase boundary in three dimensions, a boundary that cannot be accurately obtained using mean-field approaches such as boson Dynamical Mean-Field Theory. Our method also may be applied to the study of electron-phonon coupling and high-temperature superconductivity.

Abstract Author(s): Brenda Rubenstein, Shiwei Zhang, and David Reichman