The fermion density operator in the droplet bosonization picture

TL;DR

This paper develops a phase space density operator within the droplet bosonization framework, ensuring it correctly reproduces fermionic properties and energies, thus enabling bosonization of various fermionic Hamiltonians.

Contribution

It introduces a boundary operator-based density operator in droplet bosonization that accurately captures fermionic algebra and energies, expanding bosonization techniques.

Findings

Reproduces correct fermionic excitation energies

Satisfies the proper algebra and acts on the correct Hilbert space

Enables bosonization of arbitrary fermionic Hamiltonians

Abstract

We derive the phase space particle density operator in the 'droplet' picture of bosonization in terms of the boundary operator. We demonstrate that it satisfies the correct algebra and acts on the proper Hilbert space describing the underlying fermion system, and therefore it can be used to bosonize any hamiltonian or related operator. As a demonstration we show that it reproduces the correct excitation energies for a system of free fermions with arbitrary dispersion relations.