Deconfined criticality flow in the Heisenberg model with ring-exchange interactions

TL;DR

This study compares quantum phase transition flows in the J-Q model and a CP^1 representation, revealing deviations at larger sizes that challenge the second-order transition scenario and support a different transition nature.

Contribution

It provides the first direct comparison of the deconfined critical point theory with the J-Q model using the flowgram method, highlighting scale invariance violations.

Findings

Flows coincide in a broad size range, indicating mesoscopic physics agreement.

Significant deviations at larger sizes suggest violations of scale invariance.

Results challenge the second-order transition scenario in the models.

Abstract

Quantum transition points in the J -Q model---the test bed of the deconfined critical point theory---and the SU(2)-symmetric discrete noncompact CP^1 representation of the deconfined critical action are directly compared by the flowgram method. We find that the flows of two systems coincide in a broad region of linear system sizes (10 < L < 50 for the J -Q model), implying that the deconfined critical point theory correctly captures the mesoscopic physics of competition between the antiferromagnetic and valence-bond orders in quantum spin systems. At larger sizes, however, we observe significant deviations between the two flows which both demonstrate strong violations of scale invariance. This reliably rules out the second-order transition scenario in at least one of the two models and suggests the most likely explanation for the nature of the transition in the J-Q model.