Volume 78, Number 3, May 2007
Article Number 37002
Number of page(s) 6
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
Published online 11 April 2007
EPL, 78 (2007) 37002
DOI: 10.1209/0295-5075/78/37002

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

J. Jedrzejewski1 and T. Krokhmalskii2, 1

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

received 19 January 2007; accepted in final form 15 March 2007; published May 2007
published online 11 April 2007

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 $\Gamma $-functions and Appell function. Their large-distance ($\sigma $) decay rate is derived to be of the form $\sigma ^{-1}{\rm exp} (-\sigma /\xi)$. A control of the crossover from 2D to 1D system is achieved. In comparison with the isotropic case, the correlation length $\xi $ 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.

71.10.Fd - Lattice fermion models (Hubbard model, etc.) .
71.20.-b - Electron density of states and band structure of crystalline solids.

© Europhysics Letters Association 2007