Superbosonization in disorder and chaos: The role of anomalies

Abstract

Superbosonization formula aims at rigorously calculating fermionic integrals via employing supersymmetry. We derive such a supermatrix representation of superfield integrals and specify integration contours for the supermatrices. The derivation is essentially based on the supersymmetric generalization of the Itzikson-Zuber integral in the presence of anomalies in the Berezinian and shows how an integral over supervectors is eventually reduced to an integral over commuting variables. The approach is tested by calculating both one and two point correlation functions in a class of random matrix models. It is argued that the approach is capable of producing nonperturbative results in various systems with disorder, including physics of many-body localization, and other situations hosting localization phenomena.

arXiv comment14 pages, Revtex

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Cited by in corpus (2)

• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Existence of a Phase with Finite Localization Length in the Double Scaling Limit of N-Orbital Models