# Slater and Mott insulating states in the SU(6) Hubbard model

## TL;DR

This study uses large-scale quantum Monte Carlo simulations to explore the transition from Slater to Mott insulating states in the half-filled SU(6) Hubbard model, revealing a crossover from antiferromagnetic to valence bond solid order as interaction strength increases.

## Contribution

It provides the first detailed numerical analysis of the SU(6) Hubbard model, identifying the nature of phase transitions and critical exponents in this high-symmetry system.

## Key findings

- Antiferromagnetism persists in SU(2) and SU(4) but transitions to valence bond solid in SU(6).
- Single-particle gap scales linearly with U in the Mott regime.
- Critical exponents for antiferromagnetic transition are estimated as ν=0.60 and η=0.44.

## Abstract

We perform large scale projector determinant quantum Monte-Carlo simulations to study the insulating states of the half-filled SU(6) Hubbard model on the square lattice. The transition from the antiferromagnetic state to the valence bond solid state occurs as increasing the Hubbard $U$. In contrast, in the SU(2) and SU(4) cases antiferromagnetism persists throughout the entire interaction range. In the SU(6) case, antiferromagnetism starts to develop in the weak interacting regime based on the Slater mechanism of Fermi surface nesting. As $U$ passes a crossover value $U^*/t\approx 9$, the single-particle gap scales linearly with $U$, marking the onset of Mott physics. In the Mott regime, antiferromagnetism becomes to be suppressed as $U$ increases, and vanishes after $U$ passes the critical value $U_{\rm AF,c}/t=13.3\pm 0.05$. The critical exponents are obtained via critical scalings as $\nu_{\rm AF}=0.60\pm 0.02$ and $\eta_{\rm AF}=0.44\pm 0.03$. As $U$ further increases, the valence bond solid ordering appears exhibiting the anomalous dimension $\eta_{\rm VBS}=0.98\pm 0.01$.