First order phase transitions in the square lattice "easy-plane" J-Q model

TL;DR

This study investigates the nature of the quantum phase transition in an easy-plane J-Q model on a square lattice, finding it remains first order across the interpolation from easy-plane to SU(2) symmetric models.

Contribution

It demonstrates that the superfluid-VBS transition in the easy-plane J-Q model is inherently first order, contrasting with the presumed continuous transition in the SU(2) symmetric case.

Findings

First order transition weakens with increasing lambda.

No evidence of transition becoming continuous until SU(2) point.

Transition remains first order across the entire parameter range.

Abstract

We study the quantum phase transition between the superfluid and valence bond solid in "easy-plane" J-Q models on the square lattice. The Hamiltonian we study is a linear combination of two model Hamiltonians: (1) an SU(2) symmetric model, which is the well known J-Q model that does not show any direct signs of a discontinuous transition on the largest lattices and is presumed continuous, and (2) an easy plane version of the J-Q model, which shows clear evidence for a first order transition even on rather small lattices of size $L\approx16$. A parameter $0\leq\lambda\leq 1$ ($\lambda=0$ being the easy-plane model and $\lambda=1$ being the SU(2) symmetric J-Q model) allows us to smoothly interpolate between these two limiting models. We use stochastic series expansion (SSE) quantum Monte Carlo (QMC) to investigate the nature of this transition as $\lambda$ is varied - here we present studies for $\lambda=0,0.5,0.75,0.85,0.95$ and $1$. While we find that the first order transition weakens as $\lambda$ is increased from 0 to 1, we find no evidence that the transition becomes continuous until the SU(2) symmetric point, $\lambda=1$. We thus conclude that the square lattice superfluid-VBS transition in the two-component easy-plane model is generically first order.