One-dimensional model for deconfined criticality with $\mathbb{Z}_3 \times \mathbb{Z}_3$ symmetry

TL;DR

This paper explores a one-dimensional quantum spin model with $ ext{Z}_3 imes ext{Z}_3$ symmetry, providing evidence for a deconfined critical point between a VBS phase and a $ ext{Z}_3$ ferromagnet, possibly of very weakly first-order nature.

Contribution

It introduces a novel 1D model with $ ext{Z}_3 imes ext{Z}_3$ symmetry that exhibits a deconfined quantum critical point, including an exactly solvable point and analysis of the transition's nature.

Findings

Evidence for a direct transition between VBS and $ ext{Z}_3$ ferromagnet.

Finite-entanglement scaling suggests a second-order or weakly first-order transition.

Identification of an integrable model with a very long correlation length.

Abstract

We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a $\mathbb{Z}_3$ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with $\mathbb{Z}_3\times\mathbb{Z}_3$ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a $\mathbb{Z}_3$ ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order, and is part of a family of DQCP described by walking of renormalization group flows.