Exact calculation of the magnetocaloric effect in the spin-12XXZchain

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 √ T at field-induced transitions to gapped phases.

Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states

“…Exact results for the finite-temperature properties of truly quantum models are scarce, being restricted to integrable systems such as the nearestneighbor spin-1/2 Heisenberg chain [24][25][26][27][28][29], which can be solved by generalizations of the Bethe Ansatz [30,31]. Among the numerical approaches to this problem, one of the first to be used was the full exact diagonalization (ED) of the Hamiltonian in the exponentially large Hilbert space [32].…”

Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds

“…Then, one will obtain a quantity thermal average of which coincides with ξ from Eq. (26). Defining ξ 0 = Ψ|ρ 2 0 |Ψ one will obtain for ground states without translational symmetry breaking ξ 0 = (31)…”

“…It is worth mentioning two sophisticated methods which allow one to construct thermodynamic functions of integrable model -thermodynamic Bethe ansatz (TBA) 23 and quantum transfer-matrix method (QTM) 24 , however, applicability of these methods is limited to a very narrow class of in- tegrable systems, such as XXZ-Heisenberg chain with homogeneous couplings, Hubbard chain, e.t.c. Despite great successes in exact describing of thermodynamic functions for integrable models by TBA and especially by QTM 25,26 , for many other physically and principally important low-dimensional strongly correlated lattice models only laborious numerical calculations provide more or less reliable results for finite T thermodynamics. Recently, many papers have been devoted to exact solution of the low-dimensional lattice spin models with mixed Ising and Heisenberg bonds [27][28][29][30][31][32][33][34][35][36][37] or just to pure Ising counterparts of known Heisenberg models with various one-dimensional topologies of bonds [38][39][40][41][42] .…”

Magnetic Grüneisen parameter and magnetocaloric properties of a coupled spin–electron double-tetrahedral chain

“…Of particular interest is the investigation of the MCE in various one-dimensional (1D) quantum spin systems [4][5][6][7][8][9][10][11][12][13] or hybrid spin-electron models [14][15][16]. The reason is a possibility of obtaining the exact analytical or numerical results as well as a potential use of these models for the explanation of MCE data measured for real magnetic compounds.…”