The superspin approach to a disordered quantum wire in the chiral-unitary symmetry class with an arbitrary number of channels

TL;DR

This paper extends the superspin Hamiltonian approach to analyze localization in disordered quantum wires with multiple channels, providing explicit results for the density of states near the band center in the chiral-unitary symmetry class.

Contribution

It generalizes the superspin formalism from single chains to multi-channel quantum wires with arbitrary coupling, specifically addressing the chiral-unitary class.

Findings

Derived the density of states near the band center for multi-channel wires.

Confirmed agreement with the Dorokhov-Mello-Pereyra-Kumar equation results.

Extended the superspin approach to more complex quasi-one-dimensional systems.

Abstract

We use a superspin Hamiltonian defined on an infinite-dimensional Fock space with positive definite scalar product to study localization and delocalization of noninteracting spinless quasiparticles in quasi-one-dimensional quantum wires perturbed by weak quenched disorder. Past works using this approach have considered a single chain. Here, we extend the formalism to treat a quasi-one-dimensional system: a quantum wire with an arbitrary number of channels coupled by random hopping amplitudes. The computations are carried out explicitly for the case of a chiral quasi-one-dimensional wire with broken time-reversal symmetry (chiral-unitary symmetry class). By treating the space direction along the chains as imaginary time, the effects of the disorder are encoded in the time evolution induced by a single site superspin (non-Hermitian) Hamiltonian. We obtain the density of states near the band center of an infinitely long quantum wire. Our results agree with those based on the Dorokhov-Mello-Pereyra-Kumar equation for the chiral-unitary symmetry class.