Exact calculation of the magnetocaloric effect in the spin-1/2 XXZ chain

TL;DR

This paper provides exact calculations of the magnetocaloric effect in the spin-1/2 XXZ chain using quantum transfer-matrix methods, benchmarking numerical techniques and revealing significant effects near quantum phase transitions.

Contribution

It introduces an exact analytical approach to compute entropy and cooling rates in the XXZ chain, benchmarking numerical methods and analyzing universal low-temperature behaviors.

Findings

Large magnetocaloric effect near quantum phase transitions

Verification of universal low-temperature power laws

Benchmarking of numerical methods against exact results

Abstract

We calculate the entropy and cooling rate of the antiferromagnetic spin-1/2 XXZ chain under an adiabatic demagnetization process using the quantum transfer-matrix technique and non-linear integral equations. The limiting case of the Ising chain (corresponding to infinitely large anisotropy) is presented for comparison. Our exact results for the Heisenberg chain are used as a crosscheck for the numerical exact diagonalization as well as Quantum Monte Carlo simulations and allow us to benchmark the numerical methods. Close to field-induced quantum phase transitions we observe a large magnetocaloric effect. Furthermore, we verify universal low-temperature power laws in the cooling rate and entropy, in particular linear scaling of entropy with temperature T in the gapless Luttinger-liquid state and scaling as \sqrt{T} at field-induced transitions to gapped phases.