Theoretical constraints for the magnetic-dimer transition in two-dimensional spin models

TL;DR

This paper derives theoretical constraints on the excitation spectrum at quantum phase transitions in 2D spin models, predicting gapless excitations and providing evidence for a first-order transition in a specific model.

Contribution

It introduces a general theoretical framework for understanding excitation spectra at quantum critical points in short-range interacting spin systems, supported by numerical evidence.

Findings

Predicted a branch of gapless excitations at the critical point.

Provided evidence for a first-order transition in a 2D spin model with ring-exchange.

Derived constraints applicable to a broad class of spin models.

Abstract

From general arguments, that are valid for spin models with sufficiently short-range interactions, we derive strong constraints on the excitation spectrum across a continuous phase transition at zero temperature between a magnetic and a dimerized phase, that breaks the translational symmetry. From the different symmetries of the two phases, it is possible to predict, at the quantum critical point, a branch of gapless excitations, not described by standard semi-classical approaches. By using these arguments, supported by intensive numerical calculations, we obtain a rather convincing evidence in favor of a first-order transition from the ferromagnetic to the dimerized phase in the two-dimensional spin-half model with four-spin ring-exchange interaction, recently introduced by A.W. Sandvik et al. [Phys. Rev. Lett. 89, 247201 (2002)].