Quantum Magnetism, Nonequilibrium Dynamics and Quantum Simulation of Correlated Quantum Systems
von Salvatore Rosario Manmana
Datum der mündl. Prüfung:2015-06-03
Betreuer:Prof. Dr. Thomas Pruschke
Format:PDFDescription:Cumulative Habilitation thesis by S.R. Manmana
EnglischThe theoretical and experimental investigation of strongly correlated quantum systems in- and out-of-equilibrium has been a recent focus of research in condensed matter physics. In this Habilitation thesis, I present recent and future developments of the field in the context of my own contributions. A direct relation between theoretical approaches and experiments with ultracold gases and in strongly correlated materials is made, and I discuss useful microscopic models for the description of such materials (e.g., quantum magnets). The second topic of the thesis addresses the realization of quantum many body effects in ongoing experiments with ultracold gases in the context of so-called 'Quantum Simulators'. Theoretical considerations based on so-called 'numerically exact' simulations are used to make predictions for the concrete experimental implementation of such emulators for strongly correlated systems. These experiments can be performed in a very well controlled way out-of-equilibrium, which directly connects to the third topic of the thesis, the investigation of the nonequilibrium dynamics of quantum many body systems. This addresses the relaxation behavior after so-called 'Quantum Quenches' and problems related to transport, here discussed in the context of optical lattices. The three topics are bridged by the question for the realization and characterization of novel quantum states of matter. In out-of-equilibrium situations the question is addressed if such states can be identified in the relaxation behavior. As further discussed in this thesis, indeed unconventional behavior as, e.g., the formation of 'absolute negative temperatures' and the increase of particle population in the presence of repulsive interactions is realized. In equilibrium, a bouquet of interesting behavior in various systems can be revealed in the presence of strong magnetic fields. Examples are unconventional Mott insulators, phases with 'spin-nematic order' and unusual quantum critical behavior. A recent development addresses so-called topological phases which are not described in terms of a local order parameter and hence do not fall into the realm of validity of the usual Landau theory of phases and phase transitions. Questions arise for the effect of interactions, in particular also the presence of long-range interactions as realized in quantum simulators with ultracold polar molecules. The thesis demonstrates how these aspects can be addressed via numerical methods - in particular the density matrix renormalization group method - and how this approach has been leading to interesting insights into the multi-facetted behavior of correlated quantum systems.
Keywords: Habilitation; Density Matrix Renormalization Group; Strongly Correlated Quantum Systems; Quantum Many Body Systems; Nonequilibrium Dynamics; Quantum Magnetism; Quantum Simulators; Unconventional Phases of Matter; Quantum Criticality