On ground state degeneracy of \(\mathbb{Z}_ 2\) symmetric quantum spin models
type: Item
instance of: scholarly article
title: On ground state degeneracy of \(\mathbb{Z}_ 2\) symmetric quantum spin models
zbMATH Open document ID: 0783.60105
author: Taku Matsui
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1992-09-26T00:00:00Z
review text: For a class of \(\mathbb{Z}_ 2\) symmetric quantum spin Hamiltonians the proof of the ground state degeneracy is presented and the construction of pure ground states is given. First, the finite volume ground state (which is unique) is described. Then the representations of the algebra of observables on \(L^ 2\) space of Gibbs measure are studied. The states constructed are related to ground state representation. The Markov semigroup and the existence of mass gap are discussed. Finally, Heisenberg models of spin one half are considered as examples.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B20
zbMATH DE Number: 55938
zbMATH Keywords: quantum spin models
zbMATH Keywords: ground state degeneracy
zbMATH Keywords: symmetry
zbMATH Keywords: Gibbs measure
zbMATH Keywords: Markov semigroup
reviewed by: Paweł Maślanka
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195169424
OpenAlex ID: W2054030277
cites work: On the spectrum of the Heisenberg Hamiltonian
cites work: Ground states of quantum spin systems
cites work: Q3913911
cites work: Q5185817
cites work: Uniqueness of the translationally invariant ground state in quantum spin systems
cites work: A link between quantum and classical Potts models
cites work: Some problems related to Gibbs states, canonical Gibbs states and Markovian time evolutions
DOI: 10.2977/PRIMS/1195169424
Recommended article: Degenerated ground-states in a spin chain with pair interactions: a characterization by symbolic dynamics
Recommended article: Exact Ground States in Spin Systems with Orbital Degeneracy
Recommended article: Ground states of Nicolai and ${\mathbb{Z}_2}$ Nicolai models
Recommended article: Ground state of the quantum symmetric finite-size XXZ spin chain with anisotropy parameter Delta = ½
Recommended article: On the ground state of Ising models with arbitrary spin quantum number
Recommended article: On ℤ2-indices for ground states of fermionic chains
Recommended article: Spontaneous SU2(C) symmetry breaking in the ground states of quantum spin chain
Recommended article: GROUND STATE PROPERTIES OF TWO SPIN MODELS WITH EXACTLY KNOWN GROUND STATES ON THE SQUARE LATTICE
Recommended article: Q4343654
Recommended article: q-DEFORMATIONS OF QUANTUM SPIN CHAINS WITH EXACT VALENCE-BOND GROUND STATES
description: scientific article; zbMATH DE number 55938