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arXiv:1009.4411 · Journal of Statistical Mechanics Theory and Experiment

The magnetocaloric effect in integrable spin-schains

G A P Ribeiro

Published Dec 6, 2010• 8 citations
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Abstract

We study the magnetocaloric effect for the integrable antiferromagnetic high spin chain. We present an exact computation of the Grüneisen parameter, which is closely related to the magnetocaloric effect, for the quantum spin- s chain in the thermodynamical limit by means of Bethe ansatz techniques and the quantum transfer matrix approach. We have also calculated the entropy S and the isentropes in the ( H , T ) plane. We have been able to identify the quantum critical points H c ( s ) = 2/( s + 1/2) looking at the isentropes and/or the characteristic behaviour of the Grüneisen parameter.

DOI
10.1088/1742-5468/2010/12/p12016

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We calculate the entropy and cooling rate of the antiferromagnetic spin-12\frac{1}{2}21​ XXZXXZXXZ chain under an adiabatic demagnetization process using the quantum transfer-matrix technique and nonlinear 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 cross-check 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 TTT in the gapless Luttinger-liquid state and scaling as T\sqrt{T}T​ at field-induced transitions to gapped phases.
We obtained, within a path-integral formalism (mean-field variational Gaussian approximation), analytical expressions for thermodynamic quantities such as magnetization, heat capacity, and the magnetic Gr\"uneisen parameter ${\mathrm{\ensuremath{\Gamma}}}_{H}$ of the system of triplons in spin gapped quantum magnets. Near the critical temperature ${\mathrm{\ensuremath{\Gamma}}}_{H}$ is discontinuous and changes its sign upon the Bose-Einstein condensation (BEC) of triplons. We predict that in the limit of low temperature TTT and near the critical magnetic field ${H}_{c},\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{H}$ diverges as ${\mathrm{\ensuremath{\Gamma}}}_{H}\ensuremath{\sim}1/{T}^{2}$, while it scales as ${\mathrm{\ensuremath{\Gamma}}}_{H}\ensuremath{\sim}1/(H\ensuremath{-}{H}_{c})$ as the magnetic field approaches Hc{H}_{c}Hc​.
The magnetocaloric effect in the (5∕2,1)(5∕2,1)(5∕2,1) ferrimagnetic chain is investiagted using a finite-cluster solver with central spin selection to reduce finite-size effects. We found that an enhanced magnetocaloric effect occurs at the boundary of the ground-state magnetization plateau. The calculated magnetic Gr\"uneisen parameter ${\ensuremath{\Gamma}}_{H}$ exhibits strong signatures of a field-induced quantum phase transition at the critical magnetic field Hc{H}_{c}Hc​ destroying the plateau. We obtain the characteristic increase ${\ensuremath{\Gamma}}_{H}\ensuremath{\sim}{T}^{\ensuremath{-}1∕\ensuremath{\nu}z}$ near Hc{H}_{c}Hc​ and the sign change ${\ensuremath{\Gamma}}_{H}\ensuremath{\approx}\ensuremath{-}{G}_{r}∕(H\ensuremath{-}{H}_{c})$, in accordance with scaling theory predictions.