Finite temperature tensor network study of the Hubbard model on an infinite square lattice

TL;DR

This study employs a tensor network approach to simulate the Hubbard model at finite temperatures on an infinite lattice, revealing insights into spin and charge correlations relevant for ultracold atom experiments.

Contribution

It introduces a tensor network method with symmetry and high bond dimensions to accurately simulate the Hubbard model directly in the thermodynamic limit at finite temperatures.

Findings

Spin correlators show disruption of antiferromagnetic order with doping.

Charge correlators indicate hole-doublon pairs and hole-hole repulsion.

Specific heat measurements in doped regimes.

Abstract

The Hubbard model is a longstanding problem in the theory of strongly correlated electrons and a very active one in the experiments with ultracold fermionic atoms. Motivated by current and prospective quantum simulations, we apply a two-dimensional tensor network, an infinite projected entangled pair state, evolved in imaginary time by the neighborhood tensor update algorithm working directly in the thermodynamic limit. With U(1)xU(1) symmetry and the bond dimensions up to 29, we generate thermal states down to the temperature of 0.17 times the hopping rate. We obtain results for spin and charge correlators, unaffected by boundary effects. The spin correlators, measurable in prospective ultracold atoms experiments attempting to approach the thermodynamic limit, provide evidence of disruption of the antiferromagnetic background with mobile holes in a slightly doped Hubbard model. The charge correlators reveal the presence of hole-doublon pairs near half filling and signatures of hole-hole repulsion on doping. We also obtain specific heat in the slightly doped regime.