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.
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.
We calculate the entropy and cooling rate of the antiferromagnetic spin-21XXZ 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 T at field-induced transitions to gapped phases.
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.
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.
We study a spin-1/2 model with triangular XXZ clusters on the orthogonal-dimer chain in the presence of an external magnetic field. First, we discuss the case where the triangular clusters are coupled via intermediate ``classical'' Ising spins. Diagonalization of the triangular XXZ clusters yields the exact ground states; finite-temperature properties are computed exactly by an additional transfer-matrix step. A detailed analysis reveals a large variety of ground states at magnetization M equal to fractions 0, 1/4, and 1/2 of the saturation magnetization M=1. Some of these ground states break translational symmetry spontaneously and give rise to doubling of the unit cell. In a second part, we present complementary numerical data for the spin-1/2 Heisenberg model on the orthogonal-dimer chain. We analyze several examples of T=0 magnetization curves, entropy as a function of temperature T and magnetic field, and the associated magnetic cooling rate. Comparison of the two models shows that in certain situations the simplified exactly solvable model yields a qualitatively or sometimes even quantitatively accurate description of the more challenging quantum model, including a case which may be relevant to experimental observations of an enhanced magnetocaloric effect in the two-dimensional compound SrCu2(BO3)2.
In contrast to strongly frustrated classical systems, their quantum counterparts typically have a non-degenerate ground state. A counterexample is the celebrated Heisenberg sawtooth spin chain with ferromagnetic zigzag bonds J1 and competing antiferromagnetic basal bonds J2. At a quantum phase transition point ∣J2/J1∣=1/2, this model exhibits a flat one-magnon excitation band leading to a massively degenerate ground-state manifold which results in a large residual entropy. Thus, for the spin-half model, the residual entropy amounts to exactly one half of its maximum value limT→∞S(T)/N=ln2. In the present paper we study in detail the role of the spin quantum number s and the magnetic field H in the parameter region around the transition (flat-band) point. For that we use full exact diagonalization up to N=20 lattice sites and the finite-temperature Lanczos method up to N=36 sites to calculate the density of states as well as the temperature dependence of the specific heat, the entropy and the susceptibility. The study of chain lengths up to N=36 allows a careful finite-size analysis. At the flat-band point we find extremely small finite-size effects for spin s=1/2, i.e., the numerical data virtually correspond to the thermodynamic limit. In all other cases the finite-size effects are still small and become visible at very low temperatures. In a sizeable parameter region around the flat-band point the former massively degenerate ground-state manifold acts as a large manifold of low-lying excitations leading to extraordinary thermodynamic properties at the transition point as well as in its vicinity such as an additional low-temperature maximum in the specific heat. Moreover, there is a very strong influence of the magnetic field on the low-temperature thermodynamics including an enhanced magnetocaloric effect.