Exactly-solvable system of one-dimensional trapped bosons with short and long-range interactions

TL;DR

This paper presents an exactly solvable model of one-dimensional trapped bosons with short and long-range interactions, revealing diverse phases and ground states through analytical solutions and Monte Carlo simulations.

Contribution

It provides the first exact solutions for the ground state energy and wave function of 1D trapped bosons with both contact and long-range interactions, along with a detailed phase diagram.

Findings

Exact ground state energy and wave function derived

Identification of phase transitions between different regimes

Observation of Wigner crystal formation at high repulsion

Abstract

We consider trapped bosons with contact interactions as well as Coulomb repulsion or gravitational attraction in one spatial dimension. The exact ground state energy and wave function are identified in closed form together with a rich phase diagram, unveiled by Monte Carlo methods, with crossovers between different regimes. A trapped McGuire quantum soliton describes the attractive case. Weak repulsion results in an incompressible Laughlin-like fluid with flat density, well reproduced by a Gross-Pitaevskii equation with long-range interactions. Higher repulsion induces Friedel oscillation and the eventual formation of a Wigner crystal.