Statistics of disordered chains

Jean-Marie Stéphan, Frank Pollmann

We present analytical and numerical results regarding the magnetization full counting statistics (FCS) of a subsystem in the ground state of the Haldane-Shastry chain. Exact Pfaffian expressions are derived for the cumulant generating function, as well as any observable diagonal in the spin basis. In the limit of large systems, the scaling of the FCS is found to be in agreement with the Luttinger liquid theory. The same techniques are also applied to inhomogeneous deformations of the chain. This introduces a certain amount of disorder in the system; however we show numerically that this is not sufficient to flow to the random singlet phase, that corresponds to $XXZ$ chains with uncorrelated bond disorder.

Oleg Derzhko, Taras Krokhmalskii

E. Orignac, Yoshikazu Suzumura

Oleg Derzhko, Taras Krokhmalskii

A numerical approach to the study of equilibrium statistical properties of spin-1/2 XY chains is suggested. The approach is illustrated by the examining of influence of disorder on transverse dynamical susceptibility of spin-1/2 Ising chain in random transverse field.

L. P. Gor’kov, O. N. Dorokhov, Fedor V. Prigara

Francesco Fidaleo, Carlangelo Liverani

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.