Numerical studies of various Neel-VBS transitions in SU(N) anti-ferromagnets

TL;DR

This paper reviews recent numerical simulations of bipartite SU(N) spin models using quantum Monte Carlo methods, focusing on sign-problem free models for studying quantum phase transitions between Neel and VBS phases.

Contribution

It introduces a broad class of sign-problem free SU(N) spin models and demonstrates their use in unbiased quantum criticality studies on large lattices.

Findings

Successful simulation of large-scale bipartite SU(N) models

Unbiased studies of Neel-VBS quantum critical points

Overview of future directions for designer Hamiltonians

Abstract

In this manuscript we review recent developments in the numerical simulations of bipartite SU(N) spin models by quantum Monte Carlo (QMC) methods. We provide an account of a large family of newly discovered sign-problem free spin models which can be simulated in their ground states on large lattices, containing O(10^5) spins, using the stochastic series expansion method with efficient loop algorithms. One of the most important applications so far of these Hamiltonians are to unbiased studies of quantum criticality between Neel and valence bond phases in two dimensions -- a summary of this body of work is provided. The article concludes with an overview of the current status of and outlook for future studies of the "designer" Hamiltonians.