Jump to ContentJump to Main Navigation
Stochastic Processes and Random MatricesLecture Notes of the Les Houches Summer School: Volume 104, July 2015$
Users without a subscription are not able to see the full content.

Grégory Schehr, Alexander Altland, Yan V. Fyodorov, Neil O'Connell, and Leticia F. Cugliandolo

Print publication date: 2017

Print ISBN-13: 9780198797319

Published to Oxford Scholarship Online: January 2018

DOI: 10.1093/oso/9780198797319.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 21 April 2019

Quantum spin chains and classical integrable systems

Quantum spin chains and classical integrable systems

Chapter:
(p.578) 13 Quantum spin chains and classical integrable systems
Source:
Stochastic Processes and Random Matrices
Author(s):

Anton Zabrodin

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198797319.003.0013

This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0th time of the hierarchy. This implies a remarkable relation between the quantum spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, a system of algebraic equations can be obtained for the spectrum of the spin chain Hamiltonians.

Keywords:   quantum-classical correspondence, tau-functions, KP hierarchy, integrable systems, Ruijsenaars-Schneider systems

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 .