Symmetry Protected Topological Phases in Spin Ladders with Two-body Interactions

Abstract

Spin-1/2 two-legged ladders respecting inter-leg exchange symmetry and D2 spin rotation symmetry have new symmetry protected topological (SPT) phases which are different from the Haldane phase. Three of the new SPT phases are tx,ty,tz, which all have symmetry protected two-fold degenerate edge states on each end of the open boundaries. However, the edge states in different phases have different response to magnetic field. For example, the edge states in the tz phase will be split by the magnetic field along the z-direction, but not by the fields in the x- and y-directions. We give the Hamiltonian that realizes each SPT phase and demonstrate a proof-of-principle quantum simulation scheme for Hamiltonians of the t0 and tz phases based on coupled-QED-cavity ladder.

14 pages

References in corpus (32)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Efficient classical simulation of slightly entangled quantum computations
• Topological invariants of time-reversal-invariant band structures
• Quantum Spin Hall Effect
• Periodic table for topological insulators and superconductors
• Efficient simulation of one-dimensional quantum many-body systems
• Entanglement spectrum of a topological phase in one dimension
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Topological phases of fermions in one dimension
• Coherent control of an atomic collision in a cavity
• The effects of interactions on the topological classification of free fermion systems
• Quantum Many-Body Phenomena in Coupled Cavity Arrays
• Reversible state transfer between light and a single trapped atom
• Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
• Interacting topological phases and modular invariance
• Cooling to the Ground State of Axial Motion for One Atom Strongly Coupled to an Optical Cavity
• Cavity-based single atom preparation and high-fidelity hyperfine state readout
• Symmetry protected topological phases in non-interacting fermion systems
• Lossless State Detection of Single Neutral Atoms
• Interaction effects on 1D fermionic symmetry protected topological phases
• Simulation of high-spin Heisenberg models in coupled cavities
• Magnetization and dimerization profiles of the cut two-leg spin ladder and spin-1 chain
• Competing orders in the generalized Hund chain model at half-filling
• New gapped quantum phases for S=1 spin chain with D2h symmetry
• Symmetry protected topological orders of 1D spin systems with D2+T symmetry

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• Spectral and Entanglement Properties of the Bosonic Haldane Insulator
• Entanglement entropy of (3+1)D topological orders with excitations
• Symmetry-protected topological states for interacting fermions in alkaline-earth-like atoms
• Bosons with long range interactions on two-leg ladders in artificial magnetic fields
• Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• Exactly Solvable Points and Symmetry-Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice
• Topological Order Parameters of the Spin-1/2 Dimerized Heisenberg Ladder in Magnetic Field
• Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain
• Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with a four-spin interaction
• Ground-state phase diagram of a spin-1/2 frustrated XXZ ladder
• Vortex Loops and Majoranas
• Vector-spin-chirality order in a dimerized frustrated spin-1/2 chain
• Interaction driven topological phase transitions of hardcore bosons on a two-leg ladder
• Twice Hidden String Order and Competing Phases in the Spin-1/2 Kitaev-Gamma Ladder
• Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-1/2 XXZ ladder
• Symmetry protected topological phases in spin-1 ladders and their phase transitions
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Ground-state phase diagram of S = 1/2 Heisenberg model on 2D square-hexagon-octagon lattice
• Eleven Competing Phases in the Heisenberg-Gamma (J$\Gamma$) Ladder
• Spontaneous time-reversal symmetry breaking without magnetism in a $S=1$ chain
• Phase diagram of a spin-1/2 Heisenberg ladder with a chirality-chirality interaction