Effective short distance interaction in Calogero-Sutherland quantum fluids

TL;DR

This paper investigates the short-distance interactions in Calogero-Sutherland quantum fluids, revealing an attractive force between particle-hole pairs that leads to ground state destabilization and bosonic behavior emergence, explained via a conformal field theory framework.

Contribution

It identifies a dominant attractive short-range interaction in the Calogero-Sutherland model and describes its role in ground state transformation using a Bogoliubov transformation within a conformal field theory.

Findings

Discovery of an attractive interaction between opposite moving particle-hole pairs.

Demonstration of ground state destabilization leading to bosonic excitations.

Explanation of fractionalization of charge and quantum statistics in the model.

Abstract

We consider the effective conformal field theory with symmetry W-infinity x W-infinity that describes the thermodynamic limit of the Calogero-Sutherland model. In the repulsive regime of the free fermion formulation, we identify an attractive interaction between opposite moving particle-hole pairs that dominates the short distance behavior and that is proposed as responsible for the destabilization of the ground state, leading to a new one of bosonic nature. The process is described by a Bogoliubov transformation of the free fermion bilinear operators into bosonic ones, preserving the form of the W-infinity algebra but decoupling the opposite chirality terms in the hamiltonian, as expected in the low energy limit. In coordinate space this interaction has a short range component that arises due to the quantum regularization of the theory. The described dynamical process may be considered as a mechanism of the emergence of the known charge and quantum statistics fractionalization of the low lying excitations of the theory, as predicted in both first and second quantization studies.