A Mean Field Analysis of One Dimensional Quantum Liquid with Long Range Interaction

TL;DR

This paper applies bi-local mean field theory to analyze a one-dimensional quantum liquid with long-range $1/r^2$ interactions, deriving approximate ground state properties and correlation functions that closely match exact results.

Contribution

It introduces a mean field framework for long-range interacting quantum liquids and computes ground state energy and correlations with improved accuracy.

Findings

Ground state energy agrees well with exact value

Correlation exponents show weaker coupling dependence

Effective action captures long-range dynamics

Abstract

Bi-local mean field theory is applied to one dimensional quantum liquid with long range $1/r^2$ interaction, which has exact ground state wave function. We obtain a mean field solution and an effective action which expresses a long range dynamics. Based on them the ground state energy and correlation functions are computed. The ground state energy agrees fairly well with the exact value and exponents have weaker coupling constant dependence than that of partly known exact value.