Test of Conformal Invariance in One-Dimensional Quantum Liquid with Long-Range Interaction

TL;DR

This paper numerically investigates the momentum distribution in one-dimensional quantum liquids with long-range interactions, confirming conformal invariance and critical exponents' independence from density for specific interaction strengths.

Contribution

It provides numerical evidence supporting conformal invariance in 1D quantum liquids with long-range interactions at special coupling values.

Findings

Critical exponents are density-independent.

Excellent agreement with conformal finite-size scaling.

Validation of conformal invariance in long-range interacting systems.

Abstract

We numerically study the momentum distribution of one-dimensional Bose and Fermi systems with long-range interaction $g/r^2$ for the ``special'' values $g= -\frac{1}{2}, 0, 4$, singled out by random matrix theory. The critical exponents are shown to be independent of density and in excellent agreement with estimates obtained from $c=1$ conformal finite-size scaling analysis.