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Low Temperature Physics

Low-temperature properties of the XY spin chain with an impurity fragment

E. V. Ezerskaya, A. A. Chovpan

Published Oct 1, 2006• 1 citation
Publisher

Abstract

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.

DOI
10.1063/1.2364480

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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.
We present the results of our analytical and numerical study of quantum stationary states and the thermodynamics of exactly solvable finite linear spin-1/2 XX chain with one or two distorted links. The exact dispersion equations for the stationary states with one inverted spin for both cases have been derived. The corresponding spectrum consists of one quasi-continuous band and some localized impurity levels. The analytical inequalities for the values of the critical model parameters describing the appearance of local energy impurity levels above and below quasi-continuous band are obtained and analyzed. The field and the temperature dependences of the main thermodynamic characteristics of these models are studied. It is shown, that the appearance of the localized levels near the distorted links may effect significantly on the thermodynamic properties at low temperatures, leading to the additional singularities in the field and the temperature dependences of the principal thermodynamic characteristics. For example, the field dependence of z-projection of average total spin and the field dependence of the magnetization at zero temperature have the finite jumps associated with the quasi-continuous spectrum, and the impurity levels. The remnants of these jumps at rather low temperature are clearly visible. The average z-projections of the spins of distorted link(s) may decrease with the increasing of the magnetic field for some values of model parameters. The temperature dependence of the specific heat may demonstrate additional maxima at very low temperatures. The complex oscillatory pattern of the time dependence of the dynamical longitudinal pair correlation function and the autocorrelation function is associated with the finiteness of the models and the appearance of associated localized energy levels.
This is a theoretical study of quantum stationary states and thermodynamics of two exactly solvable quantum models: a finite XX-chain with an “offshoot” that is connected via ZZ-interaction (Ising) to one of the chain nodes, and two different finite XX-chains joined through an additional ZZ-spin. It is shown that the spectrum can have impurity levels localized near the impurity spin, and the conditions for their manifestation are determined. The field and temperature dependences of the main thermodynamic characteristics of the models are investigated.
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.
The characteristics of the nuclear magnetic resonance (NMR), the contributions to the spin-lattice relaxation rate, and Knight shift of the resonance position are calculated exactly for a model spin-1/21/21/2 XYXYXY chain with the magnetic impurity. It is shown that the deviations of the impurity's coupling to the chain and the effective impurity's ggg factor from the values in the host spin chain yield special features in the temperature and magnetic field behavior for these NMR characteristics. The role of impurity-induced local levels in the NMR low-energy spin dynamics of spin chains is determined.
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.