Random-exchange and random-field xy chain for s=1/2

Abstract

One of the points of interest in the study of random systems is the nature of the eigenstates, i.e., exponentially localized or extended, and the density of states. To identify the disorder-induced effects, we consider the one-dimensional s=1/2 xy models with random exchange, or random field. Using the transformation to spinless fermions, the problem is reduced to a nonlinear map, providing accurate numerical estimates for the integrated density of states and the exponential localization length. The results clearly reveal: (i) appearance of disorder-induced tails in the integrated density of states at the bottom and top of the spectrum, yielding to a characteristic field dependence of magnetization and susceptibility at zero temperature; and (ii) important differences between random-exchange and random-field models. In the random-exchange case, the middle of the band is found to be extended, while in the random-field case, corresponding to the standard Anderson model, all states are exponentially localized. This difference also affects the temperature dependence of zero-field specific heat and susceptibility as T→0.