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Absence of normal transport in an interacting disordered spin chain

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SSDW01 - Self-interacting processes

Many-body localization (MBL) is an out-of-equilibrium phase of matter featuring emergent integrability: There exists a complete set of local integrals of motion. As a result, an MBL system remembers its initial state for arbitrarily long times if the system is thermally isolated. This implies, in particular, a total absence of transport. These phenomena are a striking manifestation of the quantum, strongly self-interacting, evolution of the probability measure. Demonstrating this at the mathematical level of rigor has proven very challenging and remains unresolved. In this talk, I will present a theorem stating that the diffusion constant of such systems vanishes, indicating that transport is at most sub-diffusive. An interesting aspect of the proof is that it relies on establishing MBL in some portions of the chains that are immune from resonances. Additionally, it rules out some numerical results that suggested MBL would not exist at all. Our work represents thus a step forward in rigorously establishing the existence of the MBL phase in one-dimensional systems. From a work with W. De Roeck, L. Giacomin and O. Prosniak.

This talk is part of the Isaac Newton Institute Seminar Series series.

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