One-body density matrix in two-dimensional insulators with anisotropic hopping: Exact study of localization vs. anisotropy

¹  Institute of Theoretical Physics, University of Wrocław - pl. Maksa Borna 9, 50-204 Wrocław, Poland
²  Institute for Condensed Matter Physics - 1 Svientsitskii Str., L'viv-11, 79011, Ukraine

Received: 19 January 2007
Accepted: 15 March 2007

Abstract

We consider tight-binding electrons on a square lattice, with an anisotropic hopping intensity, and in a periodic external potential. Breaking of the translational symmetry of the system results in two bands, separated by a gap of width proportional to the unique energy parameter of the model. The off-diagonal matrix elements of the one-body reduced density matrix are exactly expressed by product of Euler's -functions and Appell function. Their large-distance () decay rate is derived to be of the form . A control of the crossover from 2D to 1D system is achieved. In comparison with the isotropic case, the correlation length varies with the gap in a strikingly different manner. In particular, it remains nonzero as the gap vanishes, in all the directions except the direction of stronger hopping intensity.