The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature

TL;DR

This paper introduces a novel Monte Carlo algorithm to study the two-dimensional Hubbard model at finite temperature, revealing distinct correlation regimes and a decoupling of spin and charge responses, with results valid for large lattices and low temperatures.

Contribution

The paper presents a new connected determinant diagrammatic Monte Carlo method enabling exact calculations of the Hubbard model at low temperatures and large lattices, uncovering correlation regimes and spin-charge decoupling.

Findings

Identified weak, strong, and intermediate coupling regimes with distinct correlation lengths.

Discovered a crossover from commensurate to incommensurate spin correlations.

Charge correlations remain short-ranged across studied temperatures.

Abstract

We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature and interaction strength. Through these quantities, we identify a weak-coupling regime, a strong-coupling regime with short-range correlations and an intermediate-coupling regime with long magnetic correlation lengths. In the spin channel, we observe an additional crossover from commensurate to incommensurate correlations. In contrast, we find charge correlations to be only short ranged for all studied temperatures, which suggests that the spin and charge responses are decoupled. These findings were obtained by a novel connected determinant diagrammatic Monte Carlo algorithm for the computation of double expansions, which we introduce in this paper. This permits us to obtain numerically exact results at unprecedentedly low temperatures $T\geq 0.067$ for interactions up to $U\leq 8$, while working on arbitrarily large lattices. Our method also allows us to gain physical insights from investigating the analytic structure of perturbative series. We connect to previous work by studying smaller lattice geometries and report substantial finite-size effects.