2017/05/22 by Tigran Sedrakyan, Tigran A. Sedrakyan, K. B. Efetov +1
Mathematics · Physics and Astronomy · #Algebra over a field #Artificial intelligence #Class (philosophy) #Computer science #Eigenvalues and eigenvectors #Generalization #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Point (geometry) #Point process #Pure mathematics #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Random matrix #Representation (politics) #Statistical physics #Superfield #Supermatrix #Supersymmetry #Theoretical and Computational Physics #Theoretical physics #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.str-el #math-ph #math.MP
paper · pdf · doi:10.1103/physrevb.96.054208
published as Phys. Rev. B 96, 054208 (2017) · 14 pages, Revtex
arxiv created 2017/05/22 · openalex publication_date 2017/08/23 · arxiv updated 2017/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The 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 Itzykson-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.