Ground states of integrable quantum liquids

TL;DR

This paper defines ground states for integrable quantum liquids using a new operator algebra, focusing on the Hubbard chain, and analyzes energy gaps and pseudoparticle states.

Contribution

It introduces a novel operator algebra framework to explicitly construct ground states for all ensembles of integrable quantum liquids, including the Hubbard chain.

Findings

Ground states can be generated from electron or hole vacua using pseudoparticle operators.

Energy gaps for non-LWS and non-HWS states are evaluated.

The exact ground state corresponds to a non-interacting pseudoparticle state.

Abstract

Based on a recently introduced operator algebra for the description of a class of integrable quantum liquids we define the ground states for all canonical ensembles of these systems. We consider the particular case of the Hubbard chain in a magnetic field and chemical potential. The ground states of all canonical ensembles of the model can be generated by acting onto the electron vacuum (densities $n<1$) or hole vacuum (densities $n>1$), suitable pseudoparticle creation operators. We also evaluate the energy gaps of the non-lowest-weight states (non - LWS's) and non-highest-weight states (non - HWS's) of the eta-spin and spin algebras relative to the corresponding ground states. For all sectors of parameter space and symmetries the {\it exact ground state} of the many-electron problem is in the pseudoparticle basis the non-interacting pseudoparticle ground state. This plays a central role in the pseudoparticle perturbation theory.