A journey into localization, integrability and thermalization

Abstract

We present here the results obtained during my PhD work. We report the study of the many body localization transition in a spin chain and the breaking of ergodicity measured in terms of return probability in a state evolution. Moreover, we introduce the Richardson model, an exactly solvable model, that turns out to be suitable for investigating the many-body localized phase. Then we turn to the analysis of the quench problem in an ensemble of random matrices. We analyze the thermalization properties and the validity of the Eigenstate Thermalization Hypothesis for the typical case, where the quench parameter explicitly breaks a Z_2 symmetry.

Ph.D. Graduation Thesis, Sissa, Trieste (Italy) 120 Pages, 48 Figures

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• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
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• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
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• Possible experimental manifestations of the many-body localization
• Cavity method for quantum spin glasses on the Bethe lattice
• Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions
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