Antiferromagnetic long range order in the uniform resonating valence bond state on square lattice

TL;DR

This study uses extensive variational Monte Carlo simulations to demonstrate that the uniform resonating valence bond state on a square lattice exhibits antiferromagnetic long-range order with a measurable ordered moment, challenging previous theoretical expectations.

Contribution

It provides the first evidence of antiferromagnetic long-range order in the uniform RVB state on a square lattice through large-scale simulations.

Findings

Antiferromagnetic long-range order confirmed in U-RVB state.

Ordered moment estimated at approximately 0.17.

Finite size scaling follows a specific power-law behavior.

Abstract

With extensive variational Monte Carlo simulation, we show that the uniform resonating valence bond state(U-RVB) on square lattice is actually antiferromagnetic long range ordered. The ordered moment is estimated to be $m\approx 0.17$. Finite size scaling analysis on lattice up to lattice size of $50\times 50$ shows that the spin structure factor at the antiferromagnetic ordering wave vector follows perfectly the $\mathrm{S}_{\mathrm{q}=(\pi,\pi)} \simeq S_{0}+\alpha (1/L)^{5/4}$ behavior, where $L$ is linear scale of the lattice. Such a behavior is quite unexpected from the slave Boson mean field treatment or the Gutzwiller approximation of the uniform RVB state.