Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases

TL;DR

This paper constructs a new fracton topological phase from layered toric codes, explores its phase diagram, introduces a $Z_N$ generalization, and analyzes phase transitions including an intermediate phase for N≥5.

Contribution

It provides a simple description of fracton excitations, introduces a $Z_N$ generalization, and studies the phase structure and transitions of layered fracton systems.

Findings

Existence of an intermediate phase for N≥5.

A solvable model interpolating between fracton and confined phases.

A new $Z_N$ generalization of the fracton phase.

Abstract

Starting from an isotropic configuration of intersecting, two-dimensional toric codes, we construct a fracton topological phase introduced in Ref. [26], which is characterized by immobile, point- like topological excitations ("fractons"), and degenerate ground-states on the torus that are locally indistinguishable. Our proposal leads to a simple description of the fracton excitations and of the ground-state as a "loop" condensate, and provides a basis for building new 3D topological orders such as a natural, $Z_{N}$ generalization of this fracton phase, which we introduce. We describe the rich phase structure of our layered $Z_{N}$ system. By invoking a lattice duality, we demonstrate that when $N \ge 5$, there is an intermediate phase that appears between the decoupled, layered system and the fracton topologically-ordered state, which opens the possibility of a continuous transition into the fracton topological phase. We conclude by presenting a solvable model, that interpolates between the fracton phase and a confined phase in which the phase transition is first-order.