A classification of pure states on quantum spin chains satisfying the split property with on-site finite group symmetries

DOI10.1090/btran/51zbMath1471.46061arXiv1908.08621OpenAlexW3127056648MaRDI QIDQ5853604

Yoshiko Ogata

Publication date: 11 March 2021

Published in: Transactions of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.08621

zbMATH Keywords

pure split statessecond cohomology class

Mathematics Subject Classification ID

States of selfadjoint operator algebras (46L30)

Related Items

Local Noether theorem for quantum lattice systems and topological invariants of gapped states, 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, An invariant of symmetry protected topological phases with on-site finite group symmetry for two-dimensional fermion systems, Matrix product operator algebras. II: Phases of matter for 1D mixed states, SPT indices emerging from translation invariance in two-dimensional quantum spin 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, A \(\mathbb{Z}_2\)-index of symmetry protected topological phases with time reversal symmetry for quantum spin chains, The classification of symmetry protected topological phases of one-dimensional fermion systems, An index for two-dimensional SPT states, Quasi-locality bounds for quantum lattice systems. II: perturbations of frustration-free spin models with gapped ground states

Cites Work

• Unnamed Item
• Unnamed Item
• Some simple C*-algebras constructed as crossed products with discrete outer automorphism groups
• Theory of operator algebras. II
• A \(\mathbb{Z}_2\)-index of symmetry protected topological phases with time reversal symmetry for quantum spin chains
• Representations of uniformly hyperfinite algebras and their associated von Neumann rings
• BOUNDEDNESS OF ENTANGLEMENT ENTROPY AND SPLIT PROPERTY OF QUANTUM SPIN CHAINS
• On discrete twisted C*-dynamical systems, Hilbert C*-modules and regularity
• Homogeneity of the Pure State Space of a Separable C^*-Algebra
• HOMOGENEITY OF THE PURE STATE SPACE FOR SEPARABLE C*-ALGEBRAS
• Inductive Limits of Finite Dimensional C ∗ -Algebras
• The split property and the symmetry breaking of the quantum spin chain.