Strong zero modes in integrable spin-S chains

Abstract

We derive exact strong zero mode (ESZM) operators for integrable spin-S chains with open boundary conditions and a boundary field. Their locality properties are generally weaker than in the previously known cases, but they still imply infinite coherence times in the vicinity of the edges. We explain how such integrable chains possess multiple ground states describing a first-order quantum phase transition, and that the odd number of such states for integer S makes the weaker locality properties necessary. We make contact with more traditional approaches by showing how the ESZM for S=1/2 acts on energy eigenstates given by solutions of the Bethe equations.

49 pages, 18 figures

References in corpus (45)

• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• On the phase structure of driven quantum systems
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Quasilocal charges in integrable lattice systems
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Topological phases with parafermions: theory and blueprints
• Competing density-wave orders in a one-dimensional hard-boson model
• Floquet generation of Majorana end modes and topological invariants
• Many-body Localization and Symmetry Protected Topological Order
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain
• Floquet symmetry-protected topological phases in cold atomic systems
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Long coherence times for edge spins
• Lattice supersymmetry and order-disorder coexistence in the tricritical Ising model
• Prethermal Strong Zero Modes and Topological Qubits
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Lifetime of almost strong edge-mode operators in one dimensional, interacting, symmetry protected topological phases
• Almost strong 0, π edge modes in clean, interacting 1D Floquet systems
• Parafermion chain with $2\pi /k$ Floquet edge modes
• Stroboscopic Symmetry-Protected Topological Phases
• Non-local space-time supersymmetry on the lattice
• Parafermionic clock models and quantum resonance
• Spin chains with dynamical lattice supersymmetry
• Symmetry enhanced boundary qubits at infinite temperature
• Strong zero modes in a class of generalised Ising spin ladders with plaquette interactions
• Haldane-gap chains in a magnetic field
• Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method
• Open XXZ chain and boundary modes at zero temperature
• Excited states nonlinear integral equations for an integrable anisotropic spin 1 chain
• Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models with Dirichlet boundary conditions
• String order parameters for 1d Floquet Symmetry Protected Topological Phases
• Kondo effect in the isotropic Heisenberg spin chain
• Observation of topological prethermal strong zero modes
• Boundary Quantum Phase Transitions in the Spin $\frac{1}{2}$ Heisenberg Chain with Boundary Magnetic Fields
• Strong zero modes in integrable quantum circuits
• Emergent strong zero mode through local Floquet engineering
• Stochastic strong zero modes and their dynamical manifestations
• The Ising dual-reflection interface: ${\mathbb{Z}}_4$ symmetry and Majorana strong zero modes
• Boundary Strong Zero Modes
• Exact strong zero modes in quantum circuits and spin chains with non-diagonal boundary conditions
• Thermodynamics in a split Hilbert space: Quantum impurity at the edge of a one-dimensional superconductor