Emptiness Formation Probability in 1D Bose Liquids

TL;DR

This paper investigates the probability of finding no particles in a segment of a 1D Bose liquid, revealing a crossover from Poisson to Gaussian behavior in a specific regime, using instanton techniques.

Contribution

It introduces a detailed analysis of EFP in 1D Bose liquids, especially in the weakly interacting regime, employing instanton methods to explore the crossover behavior.

Findings

EFP exhibits a crossover from Poisson to Gaussian behavior.

The crossover occurs in the regime $n^{-1} < R < \xi$ for weak interactions.

Quantitative analysis of EFP using instanton techniques.

Abstract

We study emptiness formation probability (EFP) in interacting 1D Bose liquids. That is the probability that a snapshot of its ground state reveals exactly zero number of particles within the interval $|x|<R$. For a weakly interacting liquid there is parametrically wide regime $n^{-1} < R <\xi$ (here $n$ is the average density and $\xi$ is the healing length), where EFP exhibits a non-trivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [A. Abanov, 2004] to study quantitative details of these regime and compare it with previously reported limited cases.