Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets

Abstract

We review the basic properties of the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, including its persistence in quasi-one-dimensional geometries. Using large-scale numerical simulations, we map out the phase diagram for a realistic model applicable to experimental Haldane compounds. We also investigate the effect of different chain coupling geometries and confirm a general mean field universality of the critical coupling times the coordination number of the lattice. Inspired by the recent development of characterization of symmetry protected topological states, of which the Haldane phase of spin-1 Heisenberg antiferromagnetic chain is a preeminent example, we provide direct evidence that the quasi-one-dimensional Haldane phase is indeed a non-trivial symmetry protected topological state.

Brief review for Modern Physics Letters B; 23 pages, 10 figures, 1 table

References in corpus (15)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Quantum computation on the edge of a symmetry-protected topological order
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Quantum computational capability of a 2D valence bond solid phase
• Field Induced Supersolid Phase in Spin-One Heisenberg Models
• A direct measurement of the Bose-Einstein Condensation universality class in NiCl${}_2$-4SC(NH${}_2$)${}_2$ at ultra-low temperatures
• Quantum Phase Diagram and Excitations for the One-Dimensional S=1 Heisenberg Antiferromagnet with Single-Ion Anisotropy
• Fragility of String Orders
• Spin Supersolid in Anisotropic Spin-One Heisenberg Chain
• Strange correlations in spin-1 Heisenberg antiferromagnets
• Magnetic and nematic orderings in spin-1 antiferromagnets with single-ion anisotropy
• Unusual Magnetic Response of an $S=1$ Antiferromagetic Linear-Chain Material

Cited by in corpus (2)

• Adiabatic physics of an exchange-coupled spin-dimer system: magnetocaloric effect, zero-point fluctuations, and possible two-dimensional universal behavior
• Disorder-induced Revival of the Bose-Einstein Condensation in Ni(Cl${}_{1-x}$Br${}_x$)${}_2$-4SC(NH${}_2$)${}_2$ at High Magnetic Fields