Complete Pseudohole and Heavy-Pseudoparticle Operator Representation for the Hubbard Chain

TL;DR

This paper develops a comprehensive operator algebra for the Hubbard chain, enabling the analysis of finite-energy excitations and spectral properties beyond traditional Bethe-ansatz solutions, with implications for understanding low-dimensional materials.

Contribution

It introduces a new pseudohole and heavy-pseudoparticle operator algebra that extends the Bethe-ansatz framework for the Hubbard chain, facilitating finite-energy spectral analysis.

Findings

Operator basis generates all Hubbard eigenstates from a single vacuum

Generalized pseudoparticle perturbation theory describes finite-energy transitions

Basis is suitable for studying finite-frequency properties in low-dimensional materials

Abstract

We introduce the pseudohole and heavy-pseudoparticle operator algebra that generates all Hubbard-chain eigenstates from a single reference vacuum. In addition to the pseudoholes already introduced for the description of the low-energy physics, this involves the heavy pseudoparticles associated with Hamiltonian eigenstates whose energy spectrum has a gap relatively to the many-electron ground state. We introduce a generalized pseudoparticle perturbation theory which describes the relevant finite-energy ground state transitions. In the present basis these excitations refer to a small density of excited pseudoparticles. Our operator basis goes beyond the Bethe-ansatz solution and it is the suitable and correct starting point for the study of the finite-frequency properties, which are of great relevance for the understanding of the unusual spectral properties detected in low-dimensional novel materials.