Quantum Phase Transition in a Heisenberg Antiferromagnet on a Square Lattice with Strong Plaquette Interactions

TL;DR

This paper investigates a quantum phase transition in a square lattice Heisenberg antiferromagnet with tunable interactions, using advanced numerical methods to accurately determine the critical point and critical exponent, confirming universality class predictions.

Contribution

It provides improved numerical estimates for the critical point and exponent in an inhomogeneous Heisenberg model, and demonstrates the effectiveness of CORE expansion for analyzing quantum criticality.

Findings

Critical point accurately estimated using Quantum Monte Carlo.

Critical exponent $ u$ consistent with 3D classical Heisenberg universality.

Effective Hamiltonian analysis via CORE yields reliable critical point estimates.

Abstract

We present numerical results for an $S=1/2$ Heisenberg antiferromagnet on a inhomogeneous square lattice with tunable interaction between spins belonging to different plaquettes. Employing Quantum Monte Carlo, we significantly improve on previous results for the the critical point separating singlet-disordered and N\'{e}el-ordered phases, and obtain an estimate for the critical exponent $\nu$ consistent with the three-dimensional classical Heisenberg universality class. Additionally, we show that a fairly accurate result for the critical point can be obtained from a Contractor Renormalization (CORE) expansion by applying a surprisingly simple analysis to the effective Hamiltonian.