A \(\mathbb{Z}_2\)-index of symmetry protected topological phases with time reversal symmetry for quantum spin chains

DOI10.1007/s00220-019-03521-5zbMath1435.81074arXiv1810.01045OpenAlexW3035604992MaRDI QIDQ2304958

Yoshiko Ogata

Publication date: 9 March 2020

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.01045

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Noncommutative dynamical systems (46L55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) General theory of (C^*)-algebras (46L05) Spinor and twistor methods applied to problems in quantum theory (81R25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Operator algebra methods applied to problems in quantum theory (81R15) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (23)

Local Noether theorem for quantum lattice systems and topological invariants of gapped states ⋮ A \(\mathbb{Z}_2\)-topological index for quasi-free fermions ⋮ The asymmetric valence-bond-solid states in quantum spin chains: The difference between odd and even spins ⋮ Non-local order parameters for fermion chains via the partial transpose ⋮ The split and approximate split property in 2D systems: stability and absence of superselection sectors ⋮ A derivation of braided C*-tensor categories from gapped ground states satisfying the approximate Haag duality ⋮ An invariant of symmetry protected topological phases with on-site finite group symmetry for two-dimensional fermion systems ⋮ A many-body index for quantum charge transport ⋮ Rigorous index theory for one-dimensional interacting topological insulators ⋮ Projector matrix product operators, anyons and higher relative commutants of subfactors ⋮ Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems ⋮ Classification of gapped ground state phases in quantum spin systems ⋮ General Lieb-Schultz-Mattis type theorems for quantum spin chains ⋮ A classification of invertible phases of bosonic quantum lattice systems in one dimension ⋮ Automorphic equivalence within gapped phases in the bulk ⋮ A \({{\mathbb{Z}}}_2\)-index of symmetry protected topological phases with reflection symmetry for quantum spin chains ⋮ Automorphic equivalence preserves the split property ⋮ Two-dimensional topological order and operator algebras ⋮ A classification of pure states on quantum spin chains satisfying the split property with on-site finite group symmetries ⋮ The classification of symmetry protected topological phases of one-dimensional fermion systems ⋮ An index for two-dimensional SPT states ⋮ An -valued index of symmetry-protected topological phases with on-site finite group symmetry for two-dimensional quantum spin systems ⋮ Quasi-locality bounds for quantum lattice systems. II: perturbations of frustration-free spin models with gapped ground states

Cites Work

• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization. III
• Automorphic equivalence within gapped phases of quantum lattice systems
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization. II
• Standard and split inclusions of von Neumann algebras
• Finitely correlated states on quantum spin chains
• Hidden symmetry breaking and the Haldane phase in \(S=1\) quantum spin chains
• Endomorphisms of \(\mathcal{B(H)}\). II: Finitely correlated states on \(\mathcal{O}_n\)
• The adiabatic theorem and linear response theory for extended quantum systems
• Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
• On gapped phases with a continuous symmetry and boundary operators
• Propagation of correlations in quantum lattice systems
• BOUNDEDNESS OF ENTANGLEMENT ENTROPY AND SPLIT PROPERTY OF QUANTUM SPIN CHAINS
• Continuous analogues of Fock space
• A Characterization of Pure Finitely Correlated States
• Endomorphisms of B(H)
• Physics and Mathematics of Quantum Many-Body Systems
• Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms
• An area law for one-dimensional quantum systems
• A classification of pure states on quantum spin chains satisfying the split property with on-site finite group symmetries
• The split property and the symmetry breaking of the quantum spin chain.
• Theory of operator algebras I.

This page was built for publication: A \(\mathbb{Z}_2\)-index of symmetry protected topological phases with time reversal symmetry for quantum spin chains