Crossover from Poisson to Wigner-Dyson Level Statistics in One-Dimensional Systems with Integrability Breaking
Abstract
We study XXZ-type Hamiltonians describing spinless interacting electrons in a finite one-dimensional lattice. If the Hamiltonian is integrable, an initial current persists indefinitely,(B.N. Narozhny, A.J. Millis, N. Andrei, Phys. Rev. B58), R2921 (1998) and references therein. raising the question of the effect of integrability-breaking interactions. We present numerical evidence, based on calculations of level statistics and autocorrelation of currents, supporting the presence of two transitions. First, at any infinitesimal integrability breaking (J_2>0), the level statistics (histogram of spacings between levels) depart immediately from the Poisson form. However, the tail remains exponential until a second transition to Wigner-Dyson statistics. We speculate on the implications of this unexpected result to coherence in quantum computing. Work supported in part by NSF through grant DMR 00081075, by the Rutgers Center for Materials Theory, and by a supercomputer grant from NPACI.
- Publication:
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APS March Meeting Abstracts
- Pub Date:
- March 2001
- Bibcode:
- 2001APS..MARQ13002R