Weakly first-order quantum phase transition between Spin Nematic and Valence Bond Crystal Order in a square lattice SU(4) fermionic model

TL;DR

This study investigates a square lattice SU(4) fermionic model revealing a weak first-order transition between spin nematic and valence bond crystal phases, with evidence of emergent U(1) symmetry indicating proximity to a deconfined quantum critical point.

Contribution

The paper demonstrates a sign-problem-free quantum Monte Carlo approach to explore phase transitions in an SU(4) fermionic model, revealing a weak first-order transition and emergent symmetries.

Findings

Evidence for spin nematic and valence bond crystal phases.

Identification of a weak first-order phase transition.

Emergence of U(1) symmetry near the transition.

Abstract

We consider a model Hamiltonian with two SU(4) fermions per site on a square lattice, showing a competition between bilinear and biquadratic interactions. This model has generated interest due to possible realizations in ultracold atom experiments and existence of spin liquid ground states. Using a basis transformation, we show that part of the phase diagram is amenable to quantum Monte Carlo simulations without a sign problem. We find evidence for spin nematic and valence bond crystalline phases, which are separated by a weak first order phase transition. A U(1) symmetry is found to emerge in the valence bond crystal histograms, suggesting proximity to a deconfined quantum critical point. Our results are obtained with the help of a loop algorithm which allows large-scale simulations of bilinear-biquadratic SO(N ) models on arbitrary lattices in a certain parameter regime.