Extended conformal symmetry of the one-dimensional Bose gas

TL;DR

This paper demonstrates that the low-energy excitations of the one-dimensional Bose gas can be described by an extended conformal algebra, providing a new effective Hamiltonian that includes interaction corrections.

Contribution

It introduces an effective Hamiltonian based on an extended conformal algebra to describe low-lying excitations of the 1D Bose gas, including interaction effects.

Findings

Effective Hamiltonian expressed via $W_{1+ ablafty}$ algebra

First interaction correction to free fermion Hamiltonian

Description valid at all orders in 1/N expansion

Abstract

We show that the low-lying excitations of the one-dimensional Bose gas are described, at all orders in a 1/N expansion and at the first order in the inverse of the coupling constant, by an effective hamiltonian written in terms of an extended conformal algebra, namely the Cartan subalgebra of the $W_{1+\infty}\times \bar{W}_{1+\infty}$ algebra. This enables us to construct the first interaction term which corrects the hamiltonian of free fermions equivalent to a hard-core boson system.