Abundance of translation invariant pure states on quantum spin chains
type: Item
instance of: scholarly article
title: Abundance of translation invariant pure states on quantum spin chains
zbMATH Open document ID: 0779.46047
DOI: 10.1007/BF00406552
published in: Letters in Mathematical Physics
publication date: 1992-11-10T00:00:00Z
review text: Let \(Z\) be a one-dimensional lattice and let \(A\) be the observable algebra corresponding to \(Z\) and describing a quantum spin chain. The authors have proved that the set of pure transition invariant states is \(w^*\)-dense in the set of all transition invariant states of \(A\). Moreover, it is shown, that every transition invariant state can be approximated by pure transition invariant states having an exponential decay of correlation.
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 82B10
Mathematics Subject Classification ID: 46N50
zbMATH DE Number: 70138
zbMATH Keywords: one-dimensional lattice
zbMATH Keywords: observable algebra
zbMATH Keywords: quantum spin chain
zbMATH Keywords: pure transition invariant states
zbMATH Keywords: exponential decay of correlation
Wikidata QID: Q62124867
author: Mark Fannes
author: Bruno Nachtergaele
author: Reinhard F. Werner
reviewed by: Jan Hamhalter
MaRDI profile type: Publication
cites work: Q3317599
cites work: Q3854185
cites work: Finitely correlated states on quantum spin chains
cites work: Finitely correlated pure states
cites work: The Poulsen simplex
cites work: A simplex with dense extreme points
cites work: An application of Bell's inequalities to a quantum state extension problem
cites work: Remarks on a quantum state extension problem
full work available at URL: https://doi.org/10.1007/bf00406552
OpenAlex ID: W1998679237
description: scientific article; zbMATH DE number 70138