Connection between low energy effective Hamiltonians and energy level statistics

Details Connection between low energy effective Hamiltonians and energy level statistics Connection between low energy effective Hamiltonians and energy level statistics

1994-10-18

arxiv.org/abs/cond-mat/9410060v1

Physics

Condensed Matter

REVTEX, 5 postscript figures at the end of the file

Scientific paper

10.1103/PhysRevLett.74.2050

We study the level statistics of a non-integrable one dimensional interacting fermionic system characterized by the GOE distribution. We calculate numerically on a finite size system the level spacing distribution $P(s)$ and the Dyson-Mehta $\Delta_3$ correlation. We observe that its low energy spectrum follows rather the Poisson distribution, characteristic of an integrable system, consistent with the fact that the low energy excitations of this system are described by the Luttinger model. We propose this Random Matrix Theory analysis as a probe for the existence and integrability of low energy effective Hamiltonians for strongly correlated systems.

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