# Zero mode protection at particle-hole symmetry: a geometric interpretation

Source: [Zero mode protection at particle-hole symmetry: a geometric interpretation](<https://www.sota2.com/research/paper/68fa3ac11e209131ce8cd508>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T00:14:45.583Z

Authors: K. Ziegler

Published: 2019-05-28T21:03:01.000Z

## Abstract

The properties of zero modes in particle-hole symmetric systems are analyzed in the presence of strong random scattering by a disordered environment. The study is based on the calculation of the time-averaged density distribution on a lattice. In particular, a flat distribution is found for strong random scattering. This result is compared with a decaying distribution for weak random scattering by an analysis of the scattering paths. In the calculation we consider the invariant measure of the average two-particle Green's function, which is related to lattice-covering self-avoiding (LCSA) strings. In particular, strong scattering is associated with LCSA loops, whereas weaker scattering is associated with open LCSA strings. Our results are a generalization of the delocalized state observed at the band center of a one-dimensional tight-binding model with random hopping by Dyson in 1953.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1905.12085>)

[PDF](<https://arxiv.org/pdf/1905.12085.pdf>)