Andrea De Luca, Antonello Scardicchio
We study the many body localization transition in a spin chain and the breaking of ergodicity measured in terms of return probability in a state evolution. In the many-body localized phase an initial quantum state evolves in a much smaller fraction of the Hilbert space than would be allowed by conservation of energy only. By the anomalous scaling of the participation ratios with system size we are led to consider the eigenfunctions in configuration space by means of the distribution of the wave function coefficients, a canonical observable in modern studies of Anderson localization. We show how the delocalized phase is less ergodic than predicted by random-matrix theory and how in the localized phase some properties of such distribution are very close to those of the Anderson model on the Bethe lattice. We finally present a criterion for the identification of the many-body localization transition based on these distributions which is quite robust and perfectly suited for numerical investigations of a broad class of problems.
View original:
http://arxiv.org/abs/1206.2342
No comments:
Post a Comment