Energy spectrum of a disordered linear chain

M. Ya. Mints

孝 朝日, 昌平 柏村

Claudette E. Cordeiro

Shiyu Wu

A formulation is presented such that the ensemble average of the diagonal elements of the Green's function for a one-dimensional disordered system can be calculated to arbitrary accuracy. The method is illustrated with an application to an isotopically disordered chain. An approximate solution to the frequency spectrum of a disordered binary chain is also discussed.

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

Binladin A. Balt, Francis N. C. Paraan

The quasi-particle excitation spectrum of an XY spin chain in a random transverse field was calculated by an exact singular value decomposition. The spectrum was found to be robust at small disorder strengths and deep within the paramagnetic phase. For larger disorder strengths, and about the ferromagnetic region, the spectrum deviated further from the quasi-excitation spectrum of the ordered chain. These deviations lead to the disorder-averaged ground state energy E0 to increase with disorder strength, even as the average field strength remains constant.