New perturbation theory of low-dimensional quantum liquids I: the pseudoparticle operator basis

TL;DR

This paper introduces a new pseudoparticle operator algebra for low-energy physics of one-dimensional quantum liquids, simplifying the analysis of excitations and transport in integrable models like the Hubbard chain.

Contribution

It develops a novel operator algebra that interprets Bethe-ansatz solutions in terms of pseudoparticles, enabling a perturbative approach to low-energy quantum liquids.

Findings

Ground state is a non-interacting pseudoparticle state.

Pseudoparticle interactions are well-behaved, allowing perturbation theory.

The approach naturally leads to a generalized Landau-liquid description.

Abstract

We introduce a new operator algebra for the description of the low-energy physics of one-dimensional, integrable, multicomponent quantum liquids. Considering the particular case of the Hubbard chain in a constant external magnetic field and with varying chemical potential, we show that at low energy its Bethe-ansatz solution can be interpreted in terms of the new {\it pseudoparticle operator algebra}. Our algebraic approach provides a concise interpretation of and justification for several recent studies of low-energy excitations and transport which have been based on detailed analyses of specific Bethe-ansatz eigenfunctions and eigenenergies. A central point is that the {\it exact ground state} of the interacting many-electron problem is the non-interacting pseudoparticle ground state. Furthermore, in the pseudoparticle basis, the quantum problem becomes perturbative, {\it i.e.}, the two-pseudoparticle forward-scattering vertices and amplitudes do not diverge, and one can define a many-pseudoparticle perturbation theory. We write the general quantum-liquid Hamiltonian in the new basis and show that the pseudoparticle-perturbation theory leads, in a natural way, to the generalized Landau-liquid approach.