Universality of Transport in Many-Body Lattice Models

Abstract: In this talk I will discuss rigorous results about the charge transport properties of gapless interacting fermionic lattice models, with a particular emphasys on the emergence of universality at the macroscopic scale. I will outline a strategy that has been used over the years to compute response functions for a class of gapless models, including one-dimensional metals and two and three-dimensional semimetals. The approach is based on the combination of: analytic continuation of real-time response functions to imaginary times; renormalization group analysis of imaginary-time correlations and resolution of the scaling limit; lattice conservation laws and Ward identities to prove universality of transport coefficients. I will focus on the application to the edge response function of interacting 2d quantum Hall systems, defined starting from the linear response ansatz. In the last part of the talk, I will discuss how the framework can be used go beyond linear response, for gapped systems at low temperatures.

mathematical physics

Audience: researchers in the discipline

One world IAMP mathematical physics seminar

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