Self-duality and bound states of the toric code model in a transverse field

Abstract

We investigate the effect of a transverse magnetic field on the toric code model. We show that this problem can be mapped onto the Xu-Moore model and thus onto the quantum compass model which are known to be self-dual. We analyze the low-energy spectrum by means of perturbative continuous unitary transformations and determine accurately the energy gaps of various symmetry sectors. Our results are in very good agreement with exact diagonalization data for all values of the parameters except at the self-dual point where level crossings are responsible for a first order phase transition between a topological phase and a polarized phase. Interestingly, bound states of two and four quasiparticles with fermionic and bosonic statistics emerge, and display dispersion relations of reduced dimensionality.

4 pages, 4 figures, typos in Eq.(4) corrected

References in corpus (10)

• A toolbox for lattice spin models with polar molecules
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Low-energy effective theory of the toric code model in a parallel field
• Superconducting Nanocircuits for Topologically Protected Qubits
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Adiabatic Preparation of Topological Order
• Anyonic interferometry and protected memories in atomic spin lattices
• First order phase transition in the anisotropic quantum orbital compass model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Nature of the Quantum Phase Transition in Quantum Compass Model

Cited by in corpus (94)

• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Area laws in a many-body localized state and its implications for topological order
• Topological quantum order: stability under local perturbations
• Robustness of a perturbed topological phase
• Topological multicritical point in the Toric Code and 3D gauge Higgs Models
• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
• The Bond-Algebraic Approach to Dualities
• Entanglement renormalization and gauge symmetry
• Quantum correlations in topological quantum phase transitions
• Topological Phase Transitions in the Golden String-Net Model
• Phase diagram of the toric code model in a parallel magnetic field
• Breakdown of a perturbed Z_N topological phase
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model
• Self-Correcting Quantum Memory in a Thermal Environment
• Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
• Fractionalization in Superconductor Josephson Junction Arrays Hinged by Quantum Spin Hall edges
• Pivot Hamiltonians as generators of symmetry and entanglement
• Electric-magnetic duality of lattice systems with topological order
• Enhanced Perturbative Continuous Unitary Transformations
• Topological quantum phase transition in bond-alternating spin-1/2 Heisenberg chains
• Compass-Heisenberg Model on the Square Lattice : Spin Order and Excitations
• Bridging Perturbative Expansions with Tensor Networks
• Fate of the cluster state on the square lattice in a magnetic field
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Matrix Product State and Quantum Phase Transitions in the One-Dimensional Extended Quantum Compass Model
• Hilbert space shattering and dynamical freezing in the quantum Ising model
• Effective and exact holographies from symmetries and dualities
• Interplay of Topological Order and Spin Glassiness in the Toric Code under Random Magnetic Fields
• Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions
• Anyonic entanglement renormalization
• Fidelity susceptibility in the two-dimensional spin-orbit models
• Robustness of a topological phase: Topological color code in parallel magnetic field
• Robust topological order in fermionic ${\mathbb{Z}}_2$ gauge theories: from Aharonov-Bohm instability to soliton-induced deconfinement
• Hidden dimer order in the quantum compass model
• Quantum phase transitions in exactly solvable one-dimensional compass models
• Nature of a topological quantum phase transition in a chiral spin liquid model
• Symmetry properties and spectra of the two-dimensional quantum compass model
• Bilayer Kitaev models: Phase diagrams and novel phases
• Exact results on the quench dynamics of the entanglement entropy in the toric code
• Correlation-Enhanced Neural Networks as Interpretable Variational Quantum States
• Persisting topological order via geometric frustration
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• Mean-field ansatz for topological phases with string tension
• Unquantized thermal Hall effect in quantum spin liquids with spinon Fermi surfaces
• Phase diagram of the $J$-$J_d$ Heisenberg Model on the Maple-Leaf Lattice: Neural networks and density matrix renormalization group
• Spin-Liquid--to--Spin-Liquid Transition in Kitaev Magnets Driven by Fractionalization
• Quantum phase transitions out of a Z2 x Z2 topological phase
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• Anyon dynamics in field-driven phases of the anisotropic Kitaev model
• On the robustness of topological quantum codes: Ising perturbation
• The Kitaev-Ising model, Transition between topological and ferromagnetic order
• Local convertibility of the ground state of the perturbed Toric code
• Competing topological orders in three dimensions: X-cube versus toric code
• Global entanglement in a topological quantum phase transition
• Spectroscopy of a topological phase
• Quasiparticles as Detector of Topological Quantum Phase Transitions
• The quantum compass chain in a transverse magnetic field
• Compass and Kitaev models -- Theory and Physical Motivations
• Thermalization of Topological Entropy after a Quantum Quench
• Bounds on universal quantum computation with perturbed 2d cluster states
• Perturbative stability and error correction thresholds of quantum codes
• Mechanism of hole propagation in the orbital compass models
• Realization of Topological Quantum Computation with surface codes
• Majorana stripe order on the surface of a three-dimensional topological insulator
• Predicting topological quantum phase transition from dynamics via multisite entanglement
• Topological Minimally Entangled States via Geometric Measure
• Quench dynamics of topological quantum phase transition in Wen-plaquette model
• Full characterization of a spin liquid phase: from topological entropy to robustness and braid statistics
• Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model
• Non-perturbative Floquet engineering of the toric-code Hamiltonian and its ground state
• Irreducible many-body correlations in topologically ordered systems
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Quantum phase transitions in the $K$-layer Ising toric code
• Energy dynamics in a generalized compass chain
• Series expansions in closed and open quantum many-body systems with multiple quasiparticle types
• String order parameters for symmetry fractionalization in an enriched toric code
• Fracton and topological order in the XY checkerboard toric code
• Quantum robustness of the toric code in a parallel field on the honeycomb and triangular lattice
• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
• One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization
• Quantum phase transitions to topological Haldane phases in spin-one chains studied by linked-cluster expansions
• Deformed quantum double realization of the toric code and beyond
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Stripping the planar Quantum Compass Model to its basics
• ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits
• Classical ground states, spin-wave and PCUT analysis of ${\mathrm{H}}_2\mathrm{SQ}$ system
• The toric code under antiferromagnetic isotropic Heisenberg interactions
• Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$\Gamma$ magnet
• Topological order on the Bloch sphere
• «Anticommuting» ${\mathbb{Z}}_2$ quantum spin liquids
• Hidden subsystem symmetry protected states in competing topological orders
• Duality in spin systems via the $SU(4)$ algebra