Speaker: 
Anatoli Polkovnikov - Boston University

Title: 
Asymptotic Birkhoff Construction of Local Integrals of Motion in a Spin Chain

Abstract:
In this talk I will analyze a mechanism of delocalization of an impurity spin (charge), which is weakly coupled to a bath. In particular, I will use a Birkhoff perturbative construction for a conserved integral of motion adiabatically connected to the impurity spin and its non-perturbative variational generalization. I will explain that generically this construction is asymptotic. It diverges due to virtual (non-resonant) processes leading to eventual delocalization of the impurity spin. The divergence is related to the Krylov complexity of the bath and is not present in non-interacting models. This construction can be equally applied to both clean and disordered systems and, in particular  indicate that many body localization in interacting models is a transient finite time/finite system size phenomenon. In the end of the talk I will review some key earlier analytic and numerical results arguing for existence of the localized phase in the thermodynamic limit and will illustrate how such conclusions were based either on uncontrolled approximations or on improper extrapolation of the numerical data.

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QuCoLiMa Talks are the weekly seminar of the collaborative research center TRR 306 QuCoLiMa (Quantum Cooperativity of Light and Matter). The talks are given by (external) experts, whose research falls within the scope of QuCoLiMa.

More information at www.qucolima.de/talks