Starts 30 Mar 2021 11:00
Ends 30 Mar 2021 12:00
Central European Time
Many-body localization is a fascinating theoretical concept describing the intricate interplay of quantum interference,i.e., localization, with many-body interaction-induced dephasing. While numerous computational tests and also several experiments have been put forward to reveal the basic concepts, the overall understanding of the phenomenon is still limit; an important contributing factor is the lack of a microscopic analytical theory.

In this talk we will survey the status and recent progress in numerical simulations of the charge dynamics in the ergodic and non-ergodic regimes of disorder. A particular emphasis will be on the long-time asymptotics of temporal phenomena in wires of a finite length: they reveal a plethora of phenomena, such as hypersensitivity to the finite system size and manifestations of multifractality in return probabilities and dephasing times.

The talk is based on the publications:

S. Nandy, FE, and S. Bera, Dephasing in strongly disordered interacting quantum wires, Phys. Rev. B 103,085105 (2021).

F. Weiner, FE, and S. Bera, Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials, Phys.Rev.B100, 104204 (2019).

S. Bera, G. De Tomasi, F. Weiner, and FE, Density Propagator for Many-Body Localization: Finite-Size Effects, Transient Subdiffusion, and Exponential Decay, Phys. Rev.Lett. 118, 196801(2017).

The ε expansion was invented almost 50 years ago and has been used extensively ever since to study aspects of renormalization group flows and critical phenomena. Its most famous applications are found in theories involving scalar fields in 4-ε dimensions. In this talk, we will discuss the structure of the ε expansion in scalar field theories and the fixed points that can be obtained within it. Our motivation is based on the goal of classifying conformal field theories in d=3 dimensions. We will describe recently discovered universal constraints obtained within the framework of the ε expansion, focusing mostly on the 4-ε case although 3-ε will also be discussed. It will be shown that a "heavy handed" way to search for fixed points yields a plethora of new fixed points that reveal aspects of the structure of the ε expansion and suggest that a classification of conformal field theories in d=3 is likely to be highly non-trivial. (Based on arXiv:1707.06165, arXiv:1810.10541 and arXiv:2010.15915.)