Symmetry properties of the ground state of the system of interacting spinless bosons

TL;DR

This paper analyzes the symmetry properties of the ground state of finite systems of interacting spinless bosons under various boundary conditions, revealing that symmetry considerations allow for both crystalline and liquid ground states at any density.

Contribution

It provides a symmetry analysis showing that both crystalline and liquid ground states are possible for Bose systems, challenging assumptions about their exclusive ground state nature.

Findings

Periodic Bose systems have constant density.

Crystalline states do not necessarily produce Bragg peaks under spherical symmetry.

Symmetry properties permit both crystalline and liquid ground states.

Abstract

We perform the symmetry analysis of the properties of the ground state of a finite system of interacting spinless bosons for the three most symmetric boundary conditions (BCs): zero BCs with spherical and circular symmetries, as well as periodic BCs. The symmetry of the system can lead to interesting properties. For instance, the density of a periodic Bose system is an exact constant: $\rho(\textbf{r})=const$. Moreover, under the perfect spherical symmetry of BCs, the crystalline state cannot produce the Bragg peaks. The main result of the article is that symmetry properties and general quantum-mechanical theorems admit equally both crystalline and liquid ground state for a Bose system of any density.