Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain

Details Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain

2005-02-17

arxiv.org/abs/cond-mat/0502431v1

Lect. Notes Phys. 645, 349-379 (2004)

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

10.1007/BFb0119598

In this contribution we review the theory of integrability of quantum systems in one spatial dimension. We introduce the basic concepts such as the Yang-Baxter equation, commuting currents, and the algebraic Bethe ansatz. Quite extensively we present the treatment of integrable quantum systems at finite temperature on the basis of a lattice path integral formulation and a suitable transfer matrix approach (quantum transfer matrix). The general method is carried out for the seminal model of the spin-1/2 $XXZ$ chain for which thermodynamic properties like specific heat, magnetic susceptibility and the finite temperature Drude weight of the thermal conductivity are derived.

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