Fracton and topological order in the XY checkerboard toric code

Abstract

We introduce the XY checkerboard toric code. It represents a generalization of the ${\mathbb{Z}}_2$ toric code with two types of star operators with $x$ and $y$ flavor and two anisotropic star sublattices forming a checkerboard lattice. The quantum phase diagram is deduced exactly by a duality transformation to two copies of self-dual Xu-Moore models, which builds on the existence of an sub-extensive number of ${\mathbb{Z}}_2$ conserved parities. For any spatial anisotropy of the star sublattices, the XY checkerboard toric code realizes two quantum phases with ${\mathbb{Z}}_2$ topological order and an intermediate phase with type-I fracton order. The properties of the fracton phase like sub-extensive ground-state degeneracy can be analytically deduced from the degenerate limit of isolated stars. For the spatially isotropic case the extension of the fracton phase vanishes. The topological phase displays anyonic excitations with restricted mobility and dimensional reduction. All phase transitions are first order.

6 pages, 4 figures

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Local stabilizer codes in three dimensions without string logical operators
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Condensate induced transitions between topologically ordered phases
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Robustness of a perturbed topological phase
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Entanglement and topological entropy of the toric code at finite temperature
• On thermalization in Kitaev's 2D model
• Adiabatic Preparation of Topological Order
• Minimum instances of topological matter in an optical plaquette
• Qudit surface codes and gauge theory with finite cyclic groups
• Experimental implementation of adiabatic passage between different topological orders
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• $U(1)$ symmetry-enriched toric code

Cited by in corpus (3)

• Symmetry-deformed toric codes and the quantum dimer model
• Absence of topological order in the $U(1)$ checkerboard toric code
• Immobile and mobile excitations of three-spin interactions on the diamond chain