Time-reversal symmetry breaking phase in the Hubbard model: a VCA study

TL;DR

This study investigates the stability of a time-reversal symmetry breaking phase in the Hubbard model using VCA, finding metastable flux phases at certain interactions and doping levels, but antiferromagnetism remains dominant near half filling.

Contribution

It provides the first VCA-based analysis of the staggered flux phase in the Hubbard model, including effects of interactions, doping, and extensions to a three-band model.

Findings

Metastable flux phases occur at intermediate U values.

Antiferromagnetic order is most stable near half filling.

Negative nearest-neighbour interactions and doping favor flux phase stability.

Abstract

We study the stability of the time-reversal symmetry breaking staggered flux phase of a single band Hubbard model, within the Variational Cluster Approach (VCA). For intermediate and small values of the interaction $U$, we find metastable solutions for the staggered flux phase, with a maximum current per bond at $U\approx 3.2$. However, allowing for antiferromagnetic and superconducting long-range order it turns out that in the region at and close to half filling the antiferromagnetic phase is the most favorable energetically. The effect of nearest-neighbour interaction is also considered. Our results show that a negative nearest-neighbour interaction and finite doping favors the stability of the staggered-flux phase. We also present preliminary results for the three-band Hubbard model obtained with a restricted set of variational parameters. For this case, no spontaneous time-reversal symmetry breaking phase is found in our calculations.