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Soviet Journal of Low Temperature Physics

Relaxation of one-dimensional spin systems in a transverse variable magnetic field

О. Б. Заславский, V. M. Tsukernik

Published Jan 1, 1983• 2 citations
Publisher

Abstract

A semiinfinite X-Y chain is considered with an impurity at the end which interacts with a transverse magnetic field. It is shown that by using a unitary transformation that includes a nonlinear canonical transformation of Fermi operators, such a system will reduce to the model of an ideal Fermi gas. The evolution of the impurity spin with time is investigated for a jump-like change in the transverse field. It is shown that the nature of the relaxation depends on the presence of a discrete level and its closeness to the edge of the continuous spectrum. The switching on and switching off of the field are analyzed. The evolution of the total spin in time is considered for an Ising chain on which a transverse circularly polarized field acts.

DOI
10.1063/10.0030816

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Soviet Journal of Low Temperature Physics•Aug 1, 1976•0 citations
A semiinfinite X-Y chain is considered with an impurity at the end which interacts with a transverse magnetic field. It is shown that by using a unitary transformation that includes a nonlinear canonical transformation of Fermi operators, such a system will reduce to the model of an ideal Fermi gas. The evolution of the impurity spin with time is investigated for a jump-like change in the transverse field. It is shown that the nature of the relaxation depends on the presence of a discrete level and its closeness to the edge of the continuous spectrum. The switching on and switching off of the field are analyzed. The evolution of the total spin in time is considered for an Ising chain on which a transverse circularly polarized field acts.
We study the time dependent behavior of the four-spin interactions Ising chain in the presence of a disordered transverse magnetic field. In order to analyze the effects of field randomness in the dynamical behavior of the system we calculate the time-dependent correlation function and the longitudinal relaxation function of the infinite chain. We consider a bi-modal distribution for the field energy strength, where one of its values equals the exchange coupling energy while the other value can be lower or higher than the coupling energy. We find that an increasing concentration of weaker fields produces an enhancement of the central mode behavior. However, when the concentration of stronger fields increases, the system undergoes a crossover from central mode to collective-type dynamics.
We study the time evolution in the transverse-field Ising chain subject to quantum quenches of finite duration, ie, a continuous change in the transverse magnetic field over a finite time. Specifically, we consider the dynamics of the total energy, one- and two-point correlation functions and Loschmidt echo during and after the quench as well as their stationary behaviour at late times. We investigate how different quench protocols affect the dynamics and identify universal properties of the relaxation.
Out-of-equilibrium behavior is explored in the one-dimensional anisotropic XY model. Initially preparing the system in the isotropic XX model with a linearly varying magnetic field to create a domain-wall magnetization profile, dynamics is generated by rapidly changing the exchange interaction anisotropy and external magnetic field. Relaxation to a nonequilibrium steady state is studied analytically at the critical transverse Ising point, where correlation functions may be computed in closed form. For arbitrary values of anisotropy and external field, an effective generalized Gibbs' ensemble is shown to accurately describe observables in the long-time limit. Additionally, we find spatial oscillations in the exponentially decaying, transverse spin-spin correlation functions with wavelength set by the magnetization jump across the initial domain wall. This wavelength depends only weakly on anisotropy and magnetic field in contrast to the current, which is highly dependent on these parameters.
The influence of a magnetic impurity on the elementary excitation spectrum of a two-dimensional Ising ferromagnet is investigated in a low transverse magnetic field. It is shown that in the case of a “ferromagnetic” impurity in a matrix of spin 1/2, from one to three local energy levels can be split off from the lower edge of the continuous spectrum of one-magnon states where the conditions for their existence impose quite strict constraints on the spin-Hamiltonian parameters. Three distinct spin configurations can be realized in the presence of an “antiferromagnetic” impurity in the crystal in the ground state. Single-magnon states of a ferromagnet are considered for those values of the spin-Hamiltonian parameters when two of them are realized. It is shown that from one to six local levels above or below the continuous spectrum band can appear, and their distance from the band edge can substantially exceed its width. Quasilocal energy levels originating within the continuous spectrum of the single-magnon states are also investigated.