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arXiv:1408.6338 · Physica A Statistical Mechanics and its Applications

On the dynamics of XY spin chains with impurities

Giuseppe Genovese

Published Apr 18, 2015• 5 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2015.04.001

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Relaxation phenomena in a class of nondissipative systems with two highly disparate time scales (i.e., Brownian systems) have unique commonalities quantifiable via two scalars. It is shown that the exactly solvable problem of the dynamics of a weakly linked impurity spin in a s=1/2 XY chain belongs to this dynamical universality class and so does that of a heavy mass in an infinite harmonic oscillator chain and a spinless quasi two-dimensional attractive Fermi gas in the long-wavelength limit. The case of the strongly linked impurity in the XY chain is also discussed along with the corresponding limits in the harmonic oscillator chain and the electron-gas problems. \textcopyright{} 1996 The American Physical Society.
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.