Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling

TL;DR

This study uses large-scale quantum Monte Carlo simulations to investigate a continuous phase transition in a 2D quantum spin model, revealing unexpected logarithmic corrections to scaling that challenge existing theoretical frameworks.

Contribution

It provides the first numerical evidence of a continuous antiferromagnet to valence-bond-solid transition with significant logarithmic corrections, questioning current deconfined quantum criticality theories.

Findings

Supports a continuous transition consistent with deconfined quantum criticality

Identifies large logarithmic corrections to scaling not previously anticipated

Suggests potential revisions to existing theoretical models for N=2 systems

Abstract

The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S=1/2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations. The results support a continuous transition of the ground state, in agreement with the theory of "deconfined" quantum criticality. There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated. This suggests that either the SU($N$) symmetric noncompact CP^(N-1) field theory for deconfined quantum criticality has to be revised, or that the theory for N=2 (as in the system studied here) differs significantly from N -> infinity (where the field theory is analytically tractable).