Volume 101, Number 3, February 2013
|Number of page(s)||6|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||18 February 2013|
Ergodicity breaking in a model showing many-body localization
1 SISSA - via Bonomea 265, 34136, Trieste, Italy, EU
2 LPT ENS - 24 rue Lhomond, 75005, Paris, France, EU
3 INFN, Sezione di Trieste - via Valerio 2, 34127, Trieste, Italy, EU
4 Abdus Salam ICTP - Strada Costiera 11, 34151, Trieste, Italy, EU
Received: 22 November 2012
Accepted: 19 January 2013
We study the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain. In the non-ergodic phase a quantum state evolves in a much smaller fraction of the Hilbert space than would be allowed by the conservation of extensive observables. By the anomalous scaling of the participation ratios with system size we are led to consider the distribution of the wave function coefficients, a standard observable in modern studies of Anderson localization. We finally present a criterion for the identification of the ergodicity-breaking (many-body localization) transition based on these distributions which is quite robust and well suited for numerical investigations of a broad class of problems.
PACS: 72.15.Rn – Localization effects (Anderson or weak localization) / 71.30.+h – Metal-insulator transitions and other electronic transitions / 37.10.Jk – Atoms in optical lattices
© EPLA, 2013
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