Nonequilibrium and statistical properties of isolated quantum many-body systemsŠuntajs, Jan (Avtor) Vidmar, Lev (Mentor) quantum chaosquantum ergodicityergodicity breaking transitionspectral form factorspectral statisticsquantum sun modeldisordered spin chainsAnderson modelAnderson localizationquantum many-body systemsmany-body localizationIn this thesis, we investigate ergodicity breaking transitions in different models of closed quantum systems with quenched disorder. Based on the quantum chaos conjecture, a quantum system is considered ergodic if the statistical properties of its eigenvalues and eigenstates comply with predictions of the random matrix theory (RMT). An ergodicity breaking quantum phase transition can occur upon tuning some appropriate model parameter, for instance the degree of disorder in the system, which causes the departure of the said statistical properties from the RMT predictions. We first analyse one dimensional disordered interacting spin-1/2 chains, which are predicted to host a transition between an ergodic and many-body localized phase. For a range of different indicators, our results consistently display a linear drift of the critical transition parameter with the system size. This casts doubt onto the existence of the many-body localized phase and raises important questions about the stability of the transition in the thermodynamic limit. We validate our numerical methods by performing benchmarks on the noninteracting three dimensional Anderson model, for which the critical parameters of the Anderson localization transition are known to high accuracy. In two dimensional variant of the same model, localization should occur trivially at any nonzero disorder in the thermodynamic limit. Due to considerable finite-size effects, finite samples may appear delocalized, however. We show that our numerical analysis of finite systems can correctly reproduce absence of localization transition in the thermodynamic limit. Finally, we propose the zero dimensional quantum sun model as the toy model of an ergodicity breaking transition in an interacting system. We corroborate analytic predictions of the transition with numerical calculations. We observe several hallmarks of a transition already in small systems and hence propose the model as a benchmark for future studies of ergodicity breaking transitions in interacting systems.20232023-01-13 08:15:02Doktorsko delo/naloga143821VisID: 130093COBISS_ID: 137047555sl