Entanglement properties of the Haldane phases: A finite system-size approach

Abstract

We study the bond-alternating Heisenberg model using the finite-size density-matrix renormalization group (DMRG) technique and analytical arguments based on the matrix product state, where we pay particular attention to the boundary-condition dependence on the entanglement spectrum of the system. We show that, in the antiperiodic boundary condition (APBC), the parity quantum numbers are equivalent to the topological invariants characterizing the topological phases protected by the bond-centered inversion and $\pi$ rotation about $z$ axis. We also show that the odd parity in the APBC, which characterizes topologically nontrivial phases, can be extracted as a two-fold degeneracy in the entanglement spectrum even with finite system size. We then determine the phase diagram of the model with the uniaxial single-ion anisotropy using the level spectroscopy method in the DMRG technique. These results not only suggest the detectability of the symmetry protected topological (SPT) phases via general twisted boundary conditions but also provide a useful and precise numerical tool for discussing the SPT phases in the exact diagonalization and DMRG techniques.

13 pages, 8 figures, accepted for publication in Physical Review B

References in corpus (6)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• Exact Analysis of Entanglement in Gapped Quantum Spin Chains
• Comparative density-matrix renormalization group study of symmetry-protected topological phases in spin-1 chain and Bose-Hubbard models
• Entanglement and Density Matrix of a Block of Spins in AKLT Model

Cited by in corpus (8)

• Critical Entanglement for the Half-Filled Extended Hubbard Model
• Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
• Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries
• Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics
• Existence of two distinct valence bond solid states in the dimerized frustrated ferromagnetic $J_1$-$J_1^{\prime }$-$J_2$ chain
• Critical spin-$\frac{1}{2}$ tetramer compound CuInVO${}_5$: Exploring the vicinity of two multimerized singlet states
• Topological Phases in Half-Integer Higher Spin $J_1$-$J_2$ Heisenberg Chains
• S=2 Quantum Spin Chain with the Biquadratic Exchange Interaction