Localization by particle–hole symmetry breaking: a loop expansion

Abstract

Abstract Localization by a broken particle–hole (PH) symmetry in a random system of non-interacting quantum particles is studied on a d-dimensional lattice. Our approach is based on a chiral symmetry argument and the corresponding invariant measure, where the latter is described by a Grassmann functional integral. Within a loop expansion we find for small loops diffusion in the case of PH symmetry. Breaking the PH symmetry results in the creation of random dimers, which suppress diffusion and lead to localization on the scale D / | μ | , where D is the effective diffusion coefficient at PH symmetry and μ is the parameter related to PH symmetry breaking.