Three-dimensional Hubbard model in the thermodynamic limit

TL;DR

This paper uses the numerical linked-cluster expansion to study the finite-temperature properties of the 3D Hubbard model in the thermodynamic limit, revealing detailed thermodynamic behavior and phase transition insights across various interaction strengths.

Contribution

It extends the NLCE to the 3D Hubbard model up to 9th order, providing new insights into low-temperature properties and phase transitions in the thermodynamic limit.

Findings

Convergence improves at higher interaction strengths, enabling low-temperature analysis.

Accurate estimates of Néel transition temperatures are obtained.

Evidence suggests possible magnetic instability near but away from half filling.

Abstract

We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperatures as low as 0.2 of the hopping amplitude in the strong-coupling regime. We show that in this regime, accurate estimates for transition temperatures to the N\'{e}el ordered phase, in agreement with the predicted asymptotic behavior, can be deduced from the low-temperature magnetic structure factor. We also find evidence for possible instability to the magnetically ordered phase away from, but close to, half filling. Our results have important implications for parametrizing fermionic systems in optical lattice experiments and for benchmarking other numerical methods.