A 'Dysonization' Scheme for Identifying Particles and Quasi-Particles Using Non-Hermitian Quantum Mechanics

TL;DR

This paper revisits Dyson's non-Hermitian approach to ferromagnetic excitations, extends it to doped antiferromagnets, and explores implications for high-temperature superconductivity using modern non-Hermitian quantum mechanics.

Contribution

It reformulates Dyson's scheme within a dual inner product framework and applies it to the t-J model for doped antiferromagnets, advancing understanding of quasi-particles in complex systems.

Findings

Recast Dyson's ferromagnet analysis with dual inner products.

Extended Dyson's scheme to doped antiferromagnets in the t-J model.

Provided insights into high-temperature superconductivity mechanisms.

Abstract

In 1956 Dyson analyzed the low-energy excitations of a ferromagnet using a Hamiltonian that was non-Hermitian with respect to the standard inner product. This allowed for a facile rendering of these excitations (known as spin waves) as weakly interacting bosonic quasi-particles. More than 50 years later, we have the full denouement of non-Hermitian quantum mechanics formalism at our disposal when considering Dyson's work, both technically and contextually. Here we recast Dyson's work on ferromagnets explicitly in terms of two inner products, with respect to which the Hamiltonian is always self-adjoint, if not manifestly "Hermitian". Then we extend his scheme to doped antiferromagnets described by the t-J model, in hopes of shedding light on the physics of high-temperature superconductivity.