Polaron versus Anderson Localization

TL;DR

The work analyzes localization in two settings—polaron localization in a deterministic lattice and Anderson localization in a disordered medium—arguing that both transitions arise from short-range interactions and exhibit translational symmetry breaking. By mapping polaron path-integral results to an imaginary-time Anderson framework and framing both problems within a renormalization-group perspective, the author suggests they belong to the same universality class at the localization transition, governed by a nontrivial fixed point and characterized by RG trajectories and critical exponents. The study highlights how retarded interactions emerge in the polaron problem and how stochastic dynamics underpin the Anderson model, proposing numerical (PIMC) and theoretical explorations to test universality and dimensional dependence, including Lyapunov exponents. If confirmed, this universality would unify distinct localization phenomena under a common RG framework, guiding future investigations across condensed matter and many-body physics.

Abstract

We compare two kinds of affine localizations in physics: the localization in a short range polaron and the one in a Wick rotated Anderson stochastic model. The conditions on the interaction potential necessary to see the transnational symmetry breaking localization phase transition is identical in the two problems. We therefore suggest that they should belong to the same universality class of the renormalization group for the localization phase transition.