New perturbation theory of low-dimensional quantum liquids II: operator description of Virasoro algebras in integrable systems

TL;DR

This paper develops a pseudoparticle operator algebra framework to represent Virasoro algebras in integrable quantum liquids, connecting low-energy spectra with conformal invariance and providing explicit operator expressions.

Contribution

It introduces a novel operator representation for Virasoro algebras using pseudoparticle operators in integrable systems, linking low-energy Hamiltonians to conformal field theory structures.

Findings

Derived explicit pseudoparticle operator expressions for Virasoro generators.

Established the pseudoparticle perturbation theory as a basis for critical Hamiltonians.

Analyzed the conformal invariance and response to curvature in the Hubbard chain.

Abstract

We show that the recently developed {\it pseudoparticle operator algebra} which generates the low-energy Hamiltonian eigenstates of multicomponent integrable systems also provides a natural operator representation for the the Virasoro algebras associated with the conformal-invariant character of the low-energy spectrum of the these models. Studying explicitly the Hubbard chain in a non-zero chemical potential and external magnetic field, we establish that the pseudoparticle perturbation theory provides a correct starting point for the construction of a suitable critical-point Hamiltonian. We derive explicit expressions in terms of pseudoparticle operators for the generators of the Virasoro algebras and the energy-momentum tensor, describe the conformal-invariant character of the critical point from the point of view of the response to curvature of the two-dimensional space-time, and discuss the relation to Kac-Moody algebras and dynamical separation.