Quantum Many-Body Simulations of the 2D Fermi-Hubbard Model in Ultracold Optical Lattices

TL;DR

This paper demonstrates the use of the exponential tensor renormalization group (XTRG) combined with determinant quantum Monte Carlo (DQMC) to accurately simulate the 2D Fermi-Hubbard model in ultracold optical lattices, matching experimental results at low temperatures.

Contribution

The study introduces a powerful combination of XTRG and DQMC methods for precise finite-temperature simulations of the 2D Fermi-Hubbard model, enabling detailed comparison with ultracold atom experiments.

Findings

Excellent agreement with experimental measurements at half-filling and doping.

Observation of sign-reversal in spin correlations due to magnetic polarons.

Identification of hole-doublon and hole-hole pairing behaviors.

Abstract

Understanding quantum many-body states of correlated electrons is one main theme in modern condensed matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, has been recently realized in ultracold optical lattices, it is highly desirable to have controlled numerical methodology to provide precise finite-temperature results upon doping, to directly compare with experiments. Here, we demonstrate the exponential tensor renormalization group (XTRG) algorithm [Phys. Rev. X 8, 031082 (2018)], complemented with independent determinant quantum Monte Carlo (DQMC) offer a powerful combination of tools for this purpose. XTRG provides full and accurate access to the density matrix and thus various spin and charge correlations, down to unprecedented low temperature of few percents of the fermion tunneling energy scale. We observe excellent agreement with ultracold fermion measurements at both half-filling and finite-doping, including the sign-reversal behavior in spin correlations due to formation of magnetic polarons, and the attractive hole-doublon and repulsive hole-hole pairs that are responsible for the peculiar bunching and antibunching behavior of the antimoments.