Approach to equilibrium in interacting flat band systems

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Systems that exhibit many-body localization (MBL) have been studied recently both theoretically and experimentally, because they can retain some memory of the initial conditions and are thus of interest for storing quantum information. MBL can be viewed as a generalization of Anderson localization to interacting systems and thus usually is discussed to occur in disordered systems. However, the possibility to achieve MBL in translationally invariant systems has been suggested and in particular, flat band systems have been considered in this context recently. Noninteracting flat band systems are characterized by the presence of flat energy dispersions and thus possess highly degenerate energy eigenstates. This in turn allows localized stationary eigenstates in the system. As a result, the flat band is a different source of localization in these systems and could equally well (instead of Anderson localization) lead to interacting many-body quantum systems that possess localization in the presence of particle-particle interactions.In this project we want to study, how such interacting flat band systems equilibrate and under what conditions they do not thermalize. In a previous work we have identified a diamond ladder in which the flat bands survive in the presence of interaction. We were able to demonstrate that the eigenstate thermalization hypothesis (ETH) is violated in this system and the participation ratio of selected initial states remains small over long times, which indicates a many-body localized state.Recently, Danieli et al have suggested a scheme, how interacting flat band Hamiltonians can be generated by unitary transformations from so-called semi-detangled Hamiltonians. Such models will be considered here. Besides testing ETH and the participation ratio we would like to determine the relaxation dynamics for inhomogeneous density distributions and see whether an unusual type of diffusion is present in these systems. We will use dynamical quantum typicality (DQT) to study the relaxation dynamics numerically.We plan to study the transition from the localized regime to an ergodic regime and how it evolves. This will be compared with the behavior known from disordered MBL systems, where subdiffusion is known to occur. Also, we plan to investigate the influence of disorder on interacting flat band systems to better understand the cross-over from flat band localization to disorder induced MBL.