Jump to ContentJump to Main Navigation
Quantum Dynamical Systems$
Users without a subscription are not able to see the full content.

Robert Alicki and Mark Fannes

Print publication date: 2001

Print ISBN-13: 9780198504009

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780198504009.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 23 April 2021

Spin Chains

Spin Chains

(p.73) 4 Spin Chains
Quantum Dynamical Systems

Robert Alicki

Mark Fannes

Oxford University Press

This chapter introduces quantum spin chains for two different purposes: prototypes of infinite quantum systems discretized in space, and general models of stochastic processes in discrete time on a discrete quantum state space. The algebra of local observables is constructed. The probability functionals, i.e. the states, are defined in terms of reduced density matrices with their compatibility relations. Several examples of shift-invariant states are discussed: product states, classical states, and limiting Gibbs states. The chapter concludes with the construction of nearest-neighbour dynamics and the need for an appropriate algebra of quasi-local observables.

Keywords:   quantum spin chain, local observable, reduced density matrix, compatibility condition, product state, classical state, Gibbs state, nearest-neighbour dynamics

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .