Z_3 Quantum Criticality in a spin-1/2 chain model

TL;DR

This paper investigates the Z_3 quantum criticality in a spin-1/2 chain model, revealing a phase transition in the three-state Potts universality class driven by a staggered transverse magnetic field.

Contribution

It demonstrates the Z_3 critical behavior in a spin chain model using bosonization, connecting low-energy properties to an effective XY model with three-fold symmetry breaking.

Findings

Identifies a Z_3 quantum critical point in the model.

Describes the phase transition as belonging to the three-state Potts universality class.

Provides a bosonization-based analysis of the critical properties.

Abstract

The stability of the magnetization $m=1/3$ plateau phase of the XXZ spin-1/2 Heisenberg chain with competing interactions is investigated upon switching on a staggered transverse magnetic field. Within a bosonization approach, it is shown that the low-energy properties of the model are described by an effective two-dimensional XY model in a three-fold symmetry-breaking field. A phase transition in the three-state Potts universality class is expected separating the $m=1/3$ plateau phase to a phase where the spins are polarized along the staggered magnetic field. The Z$_3$ critical properties of the transition are determined within the bosonization approach.