Quantum phase transitions in the -layer Ising toric code
arXiv:2201.10384 · doi:10.1103/PhysRevB.105.184425
Abstract
We investigate the quantum phase diagram of the -layer Ising toric code corresponding to layers of two-dimensional toric codes coupled by Ising interactions. While for small Ising interactions the system displays topological order originating from the toric codes in each layer, the system shows topological order in the high-Ising limit. The latter is demonstrated for general by deriving an effective low-energy model in -order degenerate perturbation theory, which is given as an effective anisotropic single-layer toric code in terms of collective pseudo-spins 1/2 refering to the two ground states of isolated Ising chain segments. For the specific cases and we apply high-order series expansions to determine the gap series in the low- and high-Ising limit. Extrapolation of the elementary energy gaps gives convincing evidence that the ground-state phase diagram consists of a single quantum critical point in the 3d Ising* universality class for both separating both types of topological order, which is consistent with former findings for the bilayer Ising toric code.
arXiv comment16 pages, 6 figures
References in corpus (52)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Local stabilizer codes in three dimensions without string logical operators
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
- Precision Islands in the Ising and Models
- Quantum Glassiness
- A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
- Condensate induced transitions between topologically ordered phases
- Exotic topological order in fractal spin liquids
- Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
- Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain
- Topological order in an exactly solvable 3D spin model
- Low-energy effective theory of the toric code model in a parallel field
- Robustness of a perturbed topological phase
- A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
- Topological multicritical point in the Toric Code and 3D gauge Higgs Models
- Fracton topological order via coupled layers
- Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
- Anyon condensation and its applications
- Topological order in a 3D toric code at finite temperature
- Machine Learning Quantum Spin Liquids with Quasi-particle Statistics
- The Structure of Operators in Effective Particle-Conserving Models
- Self-duality and bound states of the toric code model in a transverse field
- Adiabatic Preparation of Topological Order
- Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
- String and Membrane condensation on 3D lattices
- Continuous topological phase transitions between clean quantum Hall states
- Emergent Fermions and Anyons in the Kitaev Model
- Phase diagram of the toric code model in a parallel magnetic field
- Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
- Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
- Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States
- Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories
- Broken quantum symmetry and confinement phases in planar physics
- Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
- Numerical study of a transition between Z2 topologically ordered phases
- Anisotropic layer construction of anisotropic fracton models
- Bridging Perturbative Expansions with Tensor Networks
- Fate of the cluster state on the square lattice in a magnetic field
- Optimizing linked cluster expansions by white graphs
- Robustness of a topological phase: Topological color code in parallel magnetic field
- Quantum robustness of fracton phases
- The breaking of quantum double symmetries by defect condensation
- Frustrated topological symmetry breaking: geometrical frustration and anyon condensation
- Persisting topological order via geometric frustration
- Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
- Quantum robustness and phase transitions of the 3D Toric Code in a field
- Spin lattices with two-body Hamiltonians for which the ground state encodes a cluster state
- Competing topological orders in three dimensions: X-cube versus toric code
- Josephson Coupled Moore-Read States