Hamiltonian Formulation of the W-Infinity Minimal Models

TL;DR

This paper provides an explicit Hamiltonian formulation of W-infinity minimal models, connecting conformal field theories with quantum Hall edge states, and explores their physical and statistical properties.

Contribution

It introduces a Hamiltonian and Fock space framework for W-infinity minimal models, linking them to hierarchical quantum Hall states and non-Abelian anyons.

Findings

Explicit Hamiltonian description of W-infinity minimal models

Connection between constraints and quantum Hall edge excitations

Calculation of non-Abelian statistics via Coulomb Gas approach

Abstract

The W-infinity minimal models are conformal field theories which can describe the edge excitations of the hierarchical plateaus in the quantum Hall effect. In this paper, these models are described in very explicit terms by using a bosonic Fock space with constraints, or, equivalently, with a non-trivial Hamiltonian. The Fock space is that of the multi-component Abelian conformal theories, which provide another possible description of the hierarchical plateaus; in this space, the minimal models are shown to correspond to the sub-set of states which satisfy the constraints. This reduction of degrees of freedom can also be implemented by adding a relevant interaction to the Hamiltonian, leading to a renormalization-group flow between the two theories. Next, a physical interpretation of the constraints is obtained by representing the quantum incompressible Hall fluids as generalized Fermi seas. Finally, the non-Abelian statistics of the quasi-particles in the W-infinity minimal models is described by computing their correlation functions in the Coulomb Gas approach.