Finite-Temperature Phase Diagram of the Hubbard Model

TL;DR

This study maps the finite-temperature phase diagram of the 3D Hubbard model, revealing antiferromagnetic, a novel tau phase with infinite hopping, and incommensurate spin phases, while 2D shows no finite-temperature transition.

Contribution

First renormalization-group analysis of the 3D Hubbard model's finite-temperature phase diagram, identifying a new tau phase and detailed phase boundaries.

Findings

Identification of a tau phase with infinite electron hopping

Presence of a narrow phase separation near the tau phase

No finite-temperature phase transition in 2D Hubbard model

Abstract

The finite-temperature phase diagram of the Hubbard model in $d=3$ is obtained from renormalization-group analysis. It exhibits, around half filling, an antiferromagnetic phase and, between 30%--40% electron or hole doping from half filling, a new $\tau $ phase in which the electron hopping strength $t$ asymptotically becomes infinite under repeated rescalings. Next to the $\tau $ phase, a first-order phase boundary with very narrow phase separation (less than 2% jump in electron density) occurs. At temperatures above the $\tau $ phase, an incommensurate spin modulation phase is indicated. In $d=2$, we find that the Hubbard model has no phase transition at finite temperature.