Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas

TL;DR

This paper provides exact formulas for local correlations and full counting statistics in the 1D Bose gas, applicable to various states including equilibrium, quenched, and transport states, enhancing understanding of quantum many-body systems.

Contribution

It introduces exact analytic expressions for local correlations and full counting statistics in the Lieb-Liniger model for arbitrary states, covering equilibrium and non-equilibrium scenarios.

Findings

Exact formulas for n-body local correlations derived.

Results applicable to ground, thermal, and non-equilibrium states.

Explicit relation between local correlations and particle-number fluctuations.

Abstract

We derive exact analytic expressions for the $n$-body local correlations in the one-dimensional Bose gas with contact repulsive interactions (Lieb-Liniger model) in the thermodynamic limit. Our results are valid for arbitrary states of the model, including ground and thermal states, stationary states after a quantum quench, and non-equilibrium steady states arising in transport settings. Calculations for these states are explicitly presented and physical consequences are critically discussed. We also show that the $n$-body local correlations are directly related to the full counting statistics for the particle-number fluctuations in a short interval, for which we provide an explicit analytic result.