Integrable Quantum Spin Chains and Some Problems Related to Integrable Systems

1990 ◽  
pp. 153-159
Author(s):  
A. Kundu ◽  
B. Basumallick
Keyword(s):  
Integrable Systems ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Integrable Quantum

Quantum spin chains and classical integrable systems

2018 ◽  
Author(s):  
Anton Zabrodin
Keyword(s):  
Integrable Systems ◽  
Quantum Spin ◽  
Spin Chains ◽  
Algebraic Equations ◽  
Quantum Spin Chains ◽  
Many Body ◽  
Finite Dimensional ◽  
The Family ◽  
Classical Correspondence ◽  
Remarkable Relation

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.

scholarly journals Canonical Drude Weight for Non-integrable Quantum Spin Chains

2018 ◽  
Vol 172 (2) ◽  
pp. 379-397 ◽  
Author(s):  
Vieri Mastropietro ◽  
Marcello Porta
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Integrable Quantum ◽  
Drude Weight
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