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

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: $\rho (\text{r})=const$. 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.

21 pages, no figures; v2: sections are rearranged; a discussion of fractional statistics is added in section 2

References in corpus (2)

• Transition to a supersolid phase in a two-dimensional dilute gas of electron-hole pairs
• Exact crystalline solution for a one-dimensional few-boson system with point interaction