Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases

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.

12 pages, 9 figures

References in corpus (3)

• Local stabilizer codes in three dimensions without string logical operators
• Quantum mechanical and information theoretic view on classical glass transitions
• Resonating plaquette phases in large spin cold atom systems

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• Quantum Hydrodynamics of Fractonic Superfluids with Lineon Condensate: from Navier-Stokes-like Equations to Landau-like Criterion
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