Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models

TL;DR

This study uses quantum Monte Carlo simulations to precisely locate quantum critical points in two planar Heisenberg models with dimerization and quadrumerization, confirming their universality class and providing benchmarks for future research.

Contribution

The paper provides the first accurate quantum Monte Carlo estimates of critical points in dimerized and quadrumerized Heisenberg models, establishing their universality class and setting benchmarks.

Findings

Critical point for ladder model: α_c = 1.9096(2)

Critical point for plaquette model: α_c = 1.8230(2)

Models belong to 3D classical Heisenberg universality class

Abstract

We study two planar square lattice Heisenberg models with explicit dimerization or quadrumerization of the couplings in the form of ladder and plaquette arrangements. We investigate the quantum critical points of those models by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio $\alpha = J^\prime/J$. The critical point of the order-disorder quantum phase transition in the ladder model is determined as $\alpha_\mathrm{c} = 1.9096(2)$ improving on previous studies. For the plaquette model we obtain $\alpha_\mathrm{c} = 1.8230(2)$ establishing a first benchmark for this model from quantum Monte Carlo simulations. Based on those values we give further convincing evidence that the models are in the three-dimensional (3D) classical Heisenberg universality class. The results of this contribution shall be useful as references for future investigations on planar Heisenberg models such as concerning the influence of non-magnetic impurities at the quantum critical point.