Crossover temperature of the spin-1/2 XXZ chain with an impurity

TL;DR

This paper investigates how an impurity affects the low-temperature behavior of the spin-1/2 XXZ chain, revealing crossover phenomena related to impurity coupling and temperature through exact solutions.

Contribution

It provides an exact analysis of impurity effects in the XXZ chain, identifying crossover behaviors and deriving the temperature dependence of impurity susceptibility.

Findings

Crossover temperature depends on impurity coupling parameter.

Two types of crossover behaviors are identified: Kondo regime and decoupled impurity.

Analytic expression for impurity susceptibility is confirmed.

Abstract

We study exactly the effect of an impurity in the interacting quantum spin chain at low temperature by solving the integrable spin-1/2 XXZ periodic chain with an impurity through the algebraic and thermal Bethe ansatz methods. In particular, we investigate how the crossover temperature for the impurity specific heat depends on the impurity parameter, i.e. the coupling of the impurity to other spins, and show that it is consistent with the analytic expression that is obtained by setting the impurity susceptibility to be proportional to the inverse of the crossover temperature. In the model, two types of crossover behavior appear: one from the high-temperature regime to the low-temperature Kondo regime and another from the N-site homogeneous chain to the (N-1)-site chain with a decoupled free impurity spin, with respect to the temperature and the impurity parameter, respectively.