Mott transition in the $\pi$-flux SU($4$) Hubbard model on a square lattice

TL;DR

This study uses quantum Monte Carlo simulations to investigate the Mott transition in a $ ext{SU}(4)$ Hubbard model with $ ext{pi}$ flux on a square lattice, revealing a second-order transition from a Dirac semi-metal to a valence bond solid.

Contribution

It provides the first detailed numerical analysis of the $ ext{SU}(4)$ Hubbard model with $ ext{pi}$ flux, identifying the nature of the Mott transition and deriving the ring-exchange term analytically.

Findings

Identified a second-order Mott transition with $Z_4$ symmetry breaking.

Estimated the critical interaction strength and critical exponent $ exteta$.

Derived the ring-exchange term affecting strong coupling behavior.

Abstract

We employ the projector quantum Monte Carlo simulations to study the ground-state properties of the square-lattice SU(4) Hubbard model with a $\pi$ flux per plaquette. In the weak coupling regime, its ground state is in the gapless Dirac semi-metal phase. With increasing repulsive interaction, we show that, a Mott transition occurs from the semimetal to the valence bond solid, accompanied by the $Z_4$ discrete symmetry breaking. Our simulations demonstrate the existence of a second-order phase transition, which confirms the Ginzburg-Landau analysis. The phase transition point and the critical exponent $\eta$ are also estimated. To account for the effect of a $\pi$ flux on the ordering in the strong coupling regime, we analytically derive by the perturbation theory the ring-exchange term which describes the leading-order difference between the $\pi$-flux and zero-flux SU(4) Hubbard models.