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Physical review. B, Condensed matter

Effect of a magnetic field on the thermodynamics of diluteXYquantum chains

M. Macciò, A. Rettori, M. G. Pini

Published Apr 1, 1985• 7 citations
Publisher

Abstract

We investigate the effect of a magnetic field along the z\ensuremath{\rightarrow} direction on the magnetization, longitudinal susceptibility, and specific heat of the dilute XY quantum chain. The introduction of the field emphasizes the effect of the strong discretization of the modes giving rise to anomalies in the field dependence of the thermodynamic properties which should be experimentally observable at low temperatures.

DOI
10.1103/physrevb.31.4187

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We investigate the effect of a magnetic field along the z\ensuremath{\rightarrow} direction on the magnetization, longitudinal susceptibility, and specific heat of the dilute XY quantum chain. The introduction of the field emphasizes the effect of the strong discretization of the modes giving rise to anomalies in the field dependence of the thermodynamic properties which should be experimentally observable at low temperatures.
We use a pseudofermion representation to investigate strong-field anomalies of the magnetic-field (h) dependence of the specific heat (c) of a spin-1/2 XY chain doped with magnetic impurities. If at certain magnetic field the impurity-induced split-off energy levels come sufficiently close to the chemical potential of pseudofermions (zero), then at low temperatures the specific heat of the chain is significantly altered by even a small number of impurities. The impurity-induced peaks of the c(h) dependence correspond to magnetic fields in a range where the specific heat of the ideal spin-1/2 XY chains is exponentially small. They have the same physical origin, but different structure, as compared to the high-field anomalies of longitudinal magnetic susceptibility investigated previously.
Magnetic and thermodynamic properties of the anisotropic Heisenberg XXZ spin=1/2 chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at finite low temperature. To this end, we rigorously study the magnetization, magnetic susceptibility and specific heat of the model in the vicinity of three different magnetic fields including longitudinal, transverse and transverse staggered magnetic fields. The thermodynamic parameters of the model are investigated under two conditions separately: I) when the model is putted in the presence of homogeneous magnetic fields; II) when a finite inhomogeneity is considered for all applied magnetic fields in the Hamiltonian. We show that at low temperature, independent of the chain size, the magnetization curve versus longitudinal field has some plateaus, which convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization, susceptibility, and specific heat is reported in detail. We find that the inhomogeneity has a substantial effect on the thermodynamic parameters of the model under consideration.
Gapless phases in ground states of low-dimensional quantum spin systems are rather ubiquitous. Their peculiarity is a remarkable sensitivity to external perturbations due to permanent criticality of such phases manifested by a slow (power-low) decay of pair correlations and the divergence of the corresponding susceptibility. A strong influence of various defects on the properties of the system in such a phase can then be expected. Here, we consider the influence of vacancies on the thermodynamics of the simplest quantum model with a gapless phase, the isotropic spin-1/2 XX chain. The existence of the exact solution of this model gives a unique opportunity to describe in detail the dramatic effect of dilution on the gapless phase—the appearance of an infinite series of quantum phase transitions resulting from level crossing under the variation of a longitudinal magnetic field. We calculate the jumps in the field dependences of the ground-state longitudinal magnetization, susceptibility, entropy, and specific heat appearing at these transitions and show that they result in a highly nonlinear temperature dependence of these parameters at low T. Also, the effect of enhancement of the magnetization and longitudinal correlations in the dilute chain is established. The changes of the pair spin correlators under dilution are also analyzed. The universality of the mechanism of the quantum transition generation suggests that similar effects of dilution can also be expected in gapless phases of other low-dimensional quantum spin systems.
It is shown that the specific heat and susceptibility (${\ensuremath{\chi}}^{\mathrm{zz}}$) of the dilute XY\mathrm{XY}XY $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\ensuremath{-}\frac{1}{2}$ chain can be calculated by summing over the finite segments. At low temperatures the specific heat is determined by segments with an even number of spins, whereas the susceptibility is determined by segments with an odd number of spins. At low temperatures the specific heat behaves as ${(\frac{{T}_{0}}{T})}^{\frac{5}{4}}\mathrm{exp}[\ensuremath{-}2{(\frac{{T}_{0}}{T})}^{\frac{1}{2}}]$, where T0{T}_{0}T0​ is a characteristic temperature in the dilute spin system.
Abstract Magnetic and thermodynamic properties of the anisotropic XYZ spin-1/2 finite chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at low temperature. Using exact diagonalization method (ED), we study the magnetization, magnetic susceptibility, and specific heat of the model characterized in terms of the finite correlation length in the presence of three different magnetic fields including longitudinal, transverse, and transverse staggered magnetic fields. The magnetization, susceptibility, and the specific heat of the model are investigated under two conditions separately: (i) When the model is putted in the presence of homogeneous magnetic fields. (ii) When finite inhomogeneities are considered for all applied magnetic fields in the Hamiltonian. We show that for the finite-size XYZ chains at low temperature, the evident magnetization plateaus gradually convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization process, magnetic susceptibility, and specific heat are reported in detail. Our exact results illustrate that by altering the inhomogeneity parameters, magnetization plateaus gradually convert to their counterpart quasi-plateaus. The specific heat manifests Schottky-type maximum, double-peak, and triple-peak, as well as, transformation between them by varying considered inhomogeneity parameters in the Hamiltonian.