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Physical review. B, Condensed matter

Specific heat of the impure spin-1/2XYchain

Gennady Sh. Gildenblat

Published Sep 1, 1993• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.48.6179

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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.
We use a pseudofermion representation to study the formation and magnetic-field dependence of split-off energy levels in a spin-1/2XY chain with a small concentration of magnetic impurities. Of particular interest are split-off states whose energy at a certain magnetic field crosses the zero level corresponding to the chemical potential of pseudofermions. If this condition is satisfied, then at sufficiently low temperature the magnetic-field dependence of the chain susceptibility is significantly altered by even a small number of impurities.
A Green's-function method is used to obtain the exact expression for the local susceptibility of the impure spin-1/2 XY chain at zero temperature. The presence of the impurity (or boundary) affects the singularity of the magnetic field dependence of the local susceptibility. The corresponding critical exponent changes from -1/2 to +1/2 at an arbitrary distance from the impurity site. In contrast with the transverse Ising model, the critical exponent is independent of the perturbation strength. This phenomenon is related to the spatial oscillations of the local density of states in the nonideal XY chain. It is also shown that experimental investigation of the field dependence of the finite-temperature macroscopic susceptibility of the one-dimensional XY-like system (such as Cs2{\mathrm{Cs}}_{2}Cs2​CoCl4{\mathrm{CoCl}}_{4}CoCl4​) may reveal the formation of the localized states associated with impurities.
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.
Using the bosonization technique, we have studied a spin-1/2 magnetic impurity in Heisenberg chain, and shown that the impurity specific heat and spin susceptibility have an anomalous temperature dependence. The temperature dependence of the impurity specific heat is ${C}_{\mathrm{im}}(T)\ensuremath{\sim}{T}^{\ensuremath{\mu}}$, $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4\ensuremath{-}\frac{1}{g}(1\ensuremath{-}g{)}^{2}$, for gc<g<1{g}_{c}<g<1gc​<g<1. The impurity spin susceptibility has the following temperature dependence: ${\ensuremath{\chi}}_{\mathrm{im}}(T)\ensuremath{\sim}{T}^{\ensuremath{\nu}}$, $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ensuremath{-}\frac{1}{g}(1\ensuremath{-}g{)}^{2}$, for gc<g<1{g}_{c}<g<1gc​<g<1, and $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$, for $g\ensuremath{\le}{g}_{c}$, where gc{g}_{c}gc​ satisfies ${4g}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({1\ensuremath{-}g}_{c}{)}^{2}$, and ggg is a dimensionless coupling strength parameter.
The exact energy spectrum in a longitudinal magnetic field is found for an infinite XY chain (s=1∕2) with an impurity fragment. It is shown that, in addition to a continuum band and a discrete set of levels, the existence of from one to four bound states, localized at the boundaries of the impurity fragment with the main chain, is possible. The critical behavior of the local static thermodynamic characteristics and time dependence of the longitudinal dynamic correlation functions for different temperatures are studied. It is shown that local thermodynamic characteristics of the model can be influenced significantly by both the discrete levels and the bound states.