A simple anisotropic three-dimensional quantum spin liquid with fracton topological order

Abstract

We present a three-dimensional cubic lattice spin model, anisotropic in the $\hat{z}$ direction, that exhibits fracton topological order. The latter is a novel type of topological order characterized by the presence of immobile pointlike excitations, named fractons, residing at the corners of an operator with two-dimensional support. As other recent fracton models, ours exhibits a subextensive ground state degeneracy: On an $L_x\times L_y\times L_z$ three-torus, it has a $2^{2L_z}$ topological degeneracy, and an additional non-topological degeneracy equal to $2^{L_x{L}_y-2}$. The fractons can be combined into composite excitations that move either in a straight line along the $\hat{z}$ direction, or freely in the $xy$ plane at a given height $z$. While our model draws inspiration from the toric code, we demonstrate that it cannot be adiabatically connected to a layered toric code construction. Additionally, we investigate the effects of imposing open boundary conditions on our system. We find zero energy modes on the surfaces perpendicular to either the $\hat{x}$ or $\hat{y}$ directions, and their absence on the surfaces normal to $\hat{z}$. This result can be explained using the properties of the two kinds of composite two-fracton mobile excitations.

8 pages, 9 figures

References in corpus (4)

• Local stabilizer codes in three dimensions without string logical operators
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Topological order in a 3D toric code at finite temperature
• Layer construction of 3D topological states and string braiding statistics

Cited by in corpus (2)

• Correlation function diagnostics for type-I fracton phases
• Quantum robustness of fracton phases