Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian

TL;DR

This paper introduces a unitary transformation that diagonalizes the Tomonaga-Luttinger Hamiltonian, enabling a quasiparticle description applicable even with non-linear electron dispersion, and provides non-perturbative results for key physical quantities.

Contribution

It presents a novel quasiparticle representation of the Tomonaga-Luttinger model using a unitary operator, extending analysis beyond linear dispersion.

Findings

Unitary operator asymptotically diagonalizes the Hamiltonian.

Maps the system onto free fermionic quasiparticles for small interactions.

Provides non-perturbative results for free energy and density-density propagator.

Abstract

We find a unitary operator which asymptotically diagonalizes the Tomonaga-Luttinger hamiltonian of one-dimensional spinless electrons. The operator performs a Bogoliubov rotation in the space of electron-hole pairs. If bare interaction of the physical electrons is sufficiently small this transformation maps the original Tomonaga-Luttinger system on a system of free fermionic quasiparticles. Our representation is useful when the electron dispersion deviates from linear form. For such situation we obtain non-perturbative results for the electron gas free energy and the density-density propagator.