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arXiv:0912.5428 · Physical Review B

Exact calculation of the magnetocaloric effect in the spin- 12 XXZ chain

Christian Trippe, A. Honecker, Andreas Klümper, Vadim Ohanyan

Published Feb 2, 2010• 56 citations
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Abstract

We calculate the entropy and cooling rate of the antiferromagnetic spin-$\frac{1}{2}$ $XXZ$ 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 $T$ in the gapless Luttinger-liquid state and scaling as $\sqrt{T}$ at field-induced transitions to gapped phases.

DOI
10.1103/physrevb.81.054402

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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 compute the entropy of antiferromagnetic quantum spin-s chains in an external magnetic field using exact diagonalization and Quantum Monte Carlo simulations.The magnetocaloric effect, i. e., temperature variations during adiabatic field changes, can be derived from the isentropes.First, we focus on the example of the spins = 1 chain and show that one can cool by closing the Haldane gap with a magnetic field.We then move to quantum spin-s chains and demonstrate linear scaling with s close to the saturation field.In passing, we propose a new method to compute many low-lying excited states using the Lanczos recursion.
The entropy and cooling rate of the both antiferromagnetic spin-1/2 double sawtooth IsingHeisenberg model and mixed-spin (1,1/2) double sawtooth Ising-Heisenberg model on the distorted ladders are rigorously investigated under an adiabatic demagnetization process using the quantum transfer-matrix technique. The models include the XXZ interaction between the interstitial Heisenberg dimers, the Ising coupling between nearest-neighbor spins of the legs and rungs, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. Close to field-induced quantum phase transitions, we compare both models together in the ability of cooling/heating near the quantum critical points. However, we observe a large magnetocaloric effect for both models, the mixed-spin double sawtooth ladder shows much more magneticaloric efficiency than the spin-1/2 double sawtooth ladder. During an adiabatic demagnetization process it can be seen a temperature dropping in the vicinity of the zero-temperature quantum phase transitions. Various fixed values of the Isotropic and anisotropic parameters explicitly alter the quality of the magnetocaloric effect. This properties suggest double sawtooth Ising-Heisenberg ladders as promising alternative refrigerant materials for low-temperature magnetic refrigeration.
The magnetocaloric effect in the symmetric spin-1/2 Ising-Heisenberg diamond chain with the Ising four-spin interaction is investigated using the generalized decoration-iteration mapping transformation and the transfermatrix technique.The entropy and the Grüneisen parameter, which closely relate to the magnetocaloric effect, are exactly calculated to compare the capability of the system to cool in the vicinity of different field-induced ground-state phase transitions during the adiabatic demagnetization.
The magnetization curves and magnetocaloric effect during the adiabatic demagnetization of antiferromagnetic spin-1/2 XXZ Heisenberg clusters with the shape of Johnson's solids (triangular cupola, square cupola and pentagonal cupola) are investigated using the exact numerical diagonalization for different values of the exchange anisotropy ranging in between the Ising and fully isotropic limit. It is demonstrated that spin-1/2 XXZ Heisenberg cupolae display, in comparison with their Ising counterparts, at least one more magnetization plateau. The novel magnetization plateaux extends over a wider range of the magnetic fields with increasing of a quantum part of the XXZ exchange coupling at the expense of the original plateaux present in the limiting Ising case. It is shown that the spin-1/2 XXZ Heisenberg triangular and pentagonal cupolae exhibit an enhanced magnetocaloric effect in the vicinity of zero magnetic field, which makes these magnetic systems promising refrigerants for cooling down to ultra-low zero temperatures.
The quantum spin-12\frac{1}{2}21​ orthogonal-dimer chain with the Heisenberg intradimer and Ising interdimer interactions in a magnetic field is considered by a rigorous approach. The model conserves the zzz component of total spin on vertical Heisenberg bonds, and this property is used to calculate exactly the partition function using the transfer-matrix method. We have found the ground-state phase diagram of the given model in a magnetic field as well as the macroscopic degeneracy along field-induced transitions accompanied with the magnetization jumps. The model exhibits two intermediate fractional plateaux at one quarter and one half of the saturation magnetization. We have examined the effect of the exchange anisotropy in the XXZXXZXXZ Heisenberg intradimer interaction on the ground state. It is shown that the one-quarter and one-half plateaux may disappear from the magnetization curve for the ferromagnetic Heisenberg intradimer interaction. We have also studied rigorously the effect of frustrated interactions on the thermodynamic and magnetic properties of the model and show how the macroscopic degeneracy of the ground state is reflected in the low-temperature behavior of the magnetization, entropy, and specific heat. A possibility of observing enhanced magnetocaloric effect during the adiabatic demagnetization is discussed in detail.
An external magnetic field induces large relative changes in the entropy of one-dimensional quantum spin systems at finite temperatures. This leads to a magnetocaloric effect, i.e. a change in temperature during an adiabatic (de)magnetization process. Several examples of one-dimensional spin-1/2 models are studied by employing the Jordan–Wigner transformation and exact diagonalization. During an adiabatic (de)magnetization process, the temperature drops in the vicinity of a field-induced zero-temperature quantum phase transition. Comparing different levels of frustration, we find that more frustrated systems cool down to lower temperatures. For geometrically frustrated spin models a finite entropy survives down to zero temperature at certain magnetic fields. This property suggests frustrated quantum spin systems as promising alternative refrigerant materials for low-temperature magnetic refrigeration.