A New Model for Fractons, Fluxons, and Freeons
arXiv:2106.05451 · doi:10.1103/PhysRevB.104.115128
Abstract
We propose a lattice spin model on a cubic lattice that shares many of the properties of the 3D toric code and the X-cube fracton model. The model, made of Z_3 degrees of freedom at the links, has the vertex, the cube, and the plaquette terms. Being a stabilizer code the ground states are exactly solved. With only the vertex and the cube terms present, we show that the ground state degeneracy (GSD) is 3^(L3+3L-1) where L is the linear dimension of the cubic lattice. In addition to fractons, there are free vertex excitations we call the freeons. With the addition of the plaquette terms, GSD is vastly reduced to 3^3, with fracton, fluxon, and freeon excitations, among which only the freeons are deconfined. The model is called the AB model if only the vertex (A_v) and the cube (B_c) terms are present, and the ABC model if in addition the plaquette terms (C_p) are included. The AC model consisting of vertex and plaquette terms is the Z_3 3D toric code. The extensive GSD of the AB model derives from the existence of both local and non-local logical operators that connect different ground states. The latter operators are identical to the logical operators of the Z_3 X-cube model. Fracton excitations are immobile and accompanied by the creation of fluxons - plaquettes having nonzero flux. In the ABC model, such fluxon creation costs energy and ends up confining the fractons. Unlike past models of fractons, vertex excitations are free to move in any direction and pick up a non-trivial statistical phase when passing through a fluxon or a fracton cluster.
arXiv comment12 pages, 15 figures
References in corpus (28)
- Fault-tolerant quantum computation by anyons
- Good Quantum Error-Correcting Codes Exist
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- Quantum Error Correction and Orthogonal Geometry
- Local stabilizer codes in three dimensions without string logical operators
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
- Simple Quantum Error Correcting Codes
- Quantum Glassiness
- Fractons
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Quantum error-correcting codes associated with graphs
- A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
- Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
- Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
- Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
- Topological Computation without Braiding
- Fracton Models on General Three-Dimensional Manifolds
- Fracton topological order via coupled layers
- Three-dimensional topological lattice models with surface anyons
- Topological order in a 3D toric code at finite temperature
- Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
- Fractional excitations in foliated fracton phases
- String and Membrane condensation on 3D lattices
- X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
- Twisted Fracton Models in Three Dimensions
- Fracton fusion and statistics
- Braiding and Gapped Boundaries in Fracton Topological Phases
- 3-d topological quantum memory with a power-law energy barrier