Thermodynamics of impurities in the anisotropic Heisenberg spin-1/2 chain

TL;DR

This paper investigates the thermodynamics of impurities in the anisotropic Heisenberg spin-1/2 chain using theoretical and numerical methods, providing new formulas for susceptibility and insights into impurity effects at various temperatures.

Contribution

It introduces a parameter-free susceptibility formula for finite chains and analyzes impurity effects, including a non-trivial temperature dependence of the Curie constant.

Findings

Derived a susceptibility formula beyond the scaling limit.

Identified a crossover from boundary to ground state behavior.

Showed the Curie constant's complex temperature dependence.

Abstract

The thermodynamics of finite open antiferromagnetic XXZ chains is studied using field theory, Bethe Ansatz and quantum Monte Carlo methods. For the susceptibility a parameter-free result as a function of the number of sites L and temperature T beyond the scaling limit is derived. The limiting cases T/J >> 1/L (J being the exchange constant), where the boundary correction shows a logarithmically suppressed Curie behaviour, and T/J << 1/L, where a crossover to the ground state behaviour takes place, are discussed in detail. Based on this analysis we present a simple formula for the averaged susceptibility of a spin-1/2 chain doped with non-magnetic impurities. We show that the effective Curie constant has a highly non-trivial temperature dependence and shows scaling in the low-temperature limit. Finally, corrections due to intra- and interchain couplings and implications for experiments on Sr_2 Cu_{1-x}Pd_x O_{3+\delta} and related compounds are discussed.