Robust quantum transport at particle-hole symmetry

TL;DR

This paper demonstrates that quantum transport remains robust in disordered systems with particle-hole symmetry, with corrections vanishing at two-loop order, though the diffusion coefficient varies with the Hamiltonian.

Contribution

It provides a detailed perturbative analysis showing the robustness of diffusive quantum transport in particle-hole symmetric systems and links microscopic Hamiltonians to macroscopic metallic behavior.

Findings

Corrections to quantum transport vanish at two-loop order.

Diffusion coefficient depends on the specific Hamiltonian.

Quantum transport remains robust despite disorder.

Abstract

We study quantum transport in disordered systems with particle-hole symmetric Hamiltonians. The particle-hole symmetry is spontaneously broken after averaging with respect to disorder, and the resulting massless mode is treated in a random-phase representation of the invariant measure of the symmetry-group. We compute the resulting fermionic functional integral of the average two-particle Green's function in a perturbation theory around the diffusive limit. The results up to two-loop order show that the corrections vanish, indicating that the diffusive quantum transport is robust. On the other hand, the diffusion coefficient depends strongly on the particle-hole symmetric Hamiltonian we choose to study. This reveals a connection between the underlying microscopic theory and the classical long-scale metallic behaviour of these systems.