Quantum Phase Transitions between Symmetry-Enriched Fracton Phases

TL;DR

This paper develops a tensor network approach to study quantum phase transitions between different symmetry-enriched fracton phases, providing exact wavefunctions and quantum circuit constructions for these complex 3D states.

Contribution

It introduces a generic scheme using isoTNS to analyze symmetry fractionalization and phase transitions in 3D fracton models, including explicit wavefunctions and quantum circuit implementations.

Findings

Exact wavefunctions for symmetry-enriched fracton phases

Power-law correlations at criticality

Explicit quantum circuit constructions for 3D fracton states

Abstract

Topologically ordered phases exhibit further complexity in the presence of global symmetries: Their anyonic excitations may exhibit different transformation patterns under these symmetries, leading to a classification in terms of symmetry-enriched topological orders. We develop a generic scheme to study an analogous situation for three-dimensional fracton phases by means of isometric tensor network states (isoTNS) with finite bond dimension, which allow us to tune phase transitions between different symmetry fractionalization patterns. We focus on the X-Cube model, a paradigmatic fracton model hosting two types of excitations: lineons, which are mobile in a single direction only, and fractons that are immobile on their own. By deforming the local tensors of the fixed point ground state, we find a family of exact wavefunctions for which the symmetry fractionalization under an anti-unitary symmetry on both types of excitations is directly visible. These wavefunctions are non-stabilizer states and have non-vanishing correlation lengths. They even exhibit power-law correlations at criticality between two symmetry-enriched topological orders. Furthermore, the isoTNS description allows for the explicit construction of a linear-depth quantum circuit to sequentially realize these exotic 3D states on a quantum processor, including a holographic scheme using only a pair of two-dimensional qubit arrays alongside measurements. Our approach provides a construction to enrich phases with exotic topological or fracton order and to study 3D quantum phase transition with exact wavefunctions, and offers a tractable route to implement and characterize fracton order on quantum devices.