One Dimensional Chain with Long Range Hopping

Details One Dimensional Chain with Long Range Hopping One Dimensional Chain with Long Range Hopping

2001-12-23

arxiv.org/abs/cond-mat/0112437v2

Phys. Rev. B 68, 045101 (2003).

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevB.68.045101

The one-dimensional (1D) tight binding model with random nearest neighbor hopping is known to have a singularity of the density of states and of the localization length at the band center. We study numerically the effects of random long range (power-law) hopping with an ensemble averaged magnitude $\expectation{|t_{ij}|} \propto |i-j|^{-\sigma}$ in the 1D chain, while maintaining the particle-hole symmetry present in the nearest neighbor model. We find, in agreement with results of position space renormalization group techniques applied to the random XY spin chain with power-law interactions, that there is a change of behavior when the power-law exponent $\sigma$ becomes smaller than 2.

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