Extended Ashkin-Teller transition in two coupled frustrated Haldane chains

TL;DR

This paper explores a complex phase diagram of two coupled spin-1 Haldane chains, revealing an extended Ashkin-Teller quantum phase transition and various phases including plaquette, dimerized, and Haldane phases.

Contribution

It uncovers an extended Ashkin-Teller universality class transition in coupled Haldane chains and details the evolution of phases with inter-chain coupling.

Findings

Identified an extended Ashkin-Teller quantum phase transition separating plaquette and disordered phases.

Discovered the vanishing of the disorder phase and emergence of a dimerized phase with decreasing inter-chain coupling.

Revealed a quantum critical point with two copies of Wess-Zumino-Witten SU(2)$_2$ criticality at decoupled chains.

Abstract

We report an extremely rich ground state phase diagram of two spin-1 Haldane chains frustrated with a three-site exchange and coupled by the antiferromagnetic Heisenberg interaction on a zig-zag ladder. A particular feature of the phase diagram is the extended quantum phase transition in the Ashkin-Teller universality class that separates the plaquette phase, which spontaneously breaks translation symmetry, and the uniform disordered phase. The former is connected to the Haldane phase, stabilized by large inter-chain coupling, via the topological Gaussian transition. Upon decreasing the inter-chain interactions, this intermediate disorder phase vanishes, giving place to a dimerized phase separated from the plaquette phase on one side via a non-magnetic Ising transition and from the Haldane phase on the other side by a topological weak first-order transition. Finally, in the limit of two decoupled chains, we recover a quantum critical point that corresponds to two copies of the Wess-Zumino-Witten $\mathrm{SU(2)}_2$ criticality with a total central charge $c=3$.