Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-$1/2$ Heisenberg chain

Abstract

We study different phases of the one-dimensional bond-alternating spin-$1/2$ Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the infinite-size density matrix renormalization group algorithm) to obtain inequivalent projective representations of the (unbroken) symmetry groups of the model, which are used to identify the different phases. We find that the model exhibits trivial as well as symmetry-protected topological phases. The symmetry-protected topological phases are Haldane phases on even/odd bonds, which are protected by the time-reversal (acting on the spin as $\sigma \to -\sigma$), parity (permutation of the chain about a specific bond), and dihedral ($\pi$-rotations about a pair of orthogonal axes) symmetries. Additionally, we investigate the phases of the most general two-body bond-alternating spin-$1/2$ model, which respects the time-reversal, parity, and dihedral symmetries, and obtain its corresponding twelve different types of the symmetry-protected topological phases.

arXiv comment9 pages, 5 figures

References in corpus (21)

• Quantum Spin Hall Effect in Graphene
• The density-matrix renormalization group in the age of matrix product states
• Entanglement in quantum critical phenomena
• Entanglement spectrum of a topological phase in one dimension
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• The iTEBD algorithm beyond unitary evolution
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Matrix product operator representations
• Detection of Symmetry Protected Topological Phases in 1D
• The phase diagram of the anisotropic spin-2 XXZ model: an infinite system DMRG study
• An order parameter for symmetry-protected phases in one dimension
• Phase diagram and quench dynamics of the Cluster-XY spin chain
• Topological quantum phase transition in bond-alternating spin-1/2 Heisenberg chains
• Detection of Symmetry Enriched Topological Phases
• Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches
• Symmetry breaking and criticality in tensor-product states
• Local characterization of 1d topologically ordered states
• Symmetry protected topological orders of 1D spin systems with D2+T symmetry

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• Optimization schemes for unitary tensor-network circuit
• Local entanglement and String Order Parameter in dimerized models
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• Promising regimes for the observation of topological degeneracy in spin chains
• Topological phases of the compass ladder model
• Characterization of localized effective spins in gapped quantum spin chains