J. Jedrzejewski and T. Krokhmalskii 2007 EPL 78 37002 doi:10.1209/0295-5075/78/37002
J. Jedrzejewski1 and T. Krokhmalskii2,1
Show affiliationsWe 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 Γ-functions and Appell function. Their large-distance (σ) decay rate is derived to be of the form σ−1exp (−σ/ξ). A control of the crossover from 2D to 1D system is achieved. In comparison with the isotropic case, the correlation length ξ 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
Issue 3 (May 2007)
Received 19 January 2007, in final form 15 March 2007
Published 11 April 2007
J. Jedrzejewski and T. Krokhmalskii 2007 EPL 78 37002
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