Thermalization is ubiquitous to all physical systems and is an essential assumption for the postulates of statistical mechanics. Generally, every system evolves under its own dynamics and reaches thermal equilibrium. In the quantum realm, thermal equilibrium is described by the Eigenstate Thermalization Hypothesis (ETH); hence every system that thermalizes is expected to follow ETH. Moreover, the thermalization process is always manifested as transport of matter and quantum information across the system. Thermalizing quantum systems with local interactions are expected to show diffusive transport of global conserved quantities and ballistic information spreading. The vast majority of many-body systems show the typical behavior described above.
In this thesis, we study two mechanisms that break the standard picture of quantum thermalization. On the one hand, information spreading may be faster in the presence of long-range interactions. By simulating the Lieb-Robinson bounds in a spin chain with power-law decaying interactions, we distinguish the regime where the long-range character of the interactions becomes irrelevant for information spreading. On the other hand, the interplay of disorder and interactions can slow down transport, entering a sub-diffusive regime. We study this dynamical regime in an Anderson model on random regular graphs, where the emergence of a sub-diffusive regime before the localization transition is highly debated. Looking at long-range spectral correlations, we found that the sub-diffusive regime may be extended over the whole thermal phase of the model.
Moreover, when disorder is strong enough, quantum many-body systems can undergo an ergodicity breaking transition to a many-body localized (MBL) phase. These systems do not follow ETH, so they present a challenge for conventional statistical mechanics. In particular, we study how the structure of local operator eigenstate matrix elements (central assumption of ETH) change between the thermal and MBL phase. A complete characterization of matrix elements of correlation functions is achieved via strong disorder quasi-degenerate perturbation theory. Furthermore, we study the MBL transition mechanism, which is still an open question due to the limitations of the available techniques for addressing that regime. Focusing on the avalanche mechanism, we simulate MBL spin chains coupled to a finite and infinite thermal bath. We could estimate the thermalization rate, which behaves as an order parameter and provide bounds for the actual critical disorder in the thermodynamic limit. We propose the existence of an intermediate MBL ``regime' where the system is slowly de-localizing, but relevant time scales are out-of-reach for current experiments and numerical simulations.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:82599 |
| Date | 08 December 2022 |
| Creators | Colmenárez, Luis |
| Contributors | Luitz, David, Moessner, Roderich, Ketzmerick, Roland, Bar Lev, Yevgeny, Technische Universität Dresden, Max Planck Institute for the Physics of Complex Systems |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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