Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model

TL;DR

This study uses quantum Monte Carlo simulations to analyze the critical behavior of a two-dimensional dimerized quantum Heisenberg model, revealing evidence of an unconventional universality class differing from the classical Heisenberg model.

Contribution

It provides the first detailed numerical evidence that the critical exponents of the $J$-$J^$ model do not match the classical Heisenberg universality class, suggesting nontrivial quantum critical excitations.

Findings

Critical point at =2.5196(2) determined by finite-size scaling.

Critical exponents differ from the 3D classical Heisenberg universality class.

Supports the existence of nontrivial critical excitations at the quantum critical point.

Abstract

The two-dimensional $J$-$J^\prime$ dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio \hbox{$\alpha=J^\prime/J$}. The critical point of the order-disorder quantum phase transition in the $J$-$J^\prime$ model is determined as \hbox{$\alpha_\mathrm{c}=2.5196(2)$} by finite-size scaling for up to approximately $10 000$ quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the $J$-$J^\prime$ model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.