Can a crystal be the ground state of a Bose system?

Abstract

It is usually assumed that the Bose crystal at $T=0$ corresponds to the genuine ground state of a Bose system, i.e., this state is non-degenerate and is described by the wave function without nodes. By means of symmetry analysis we show that the ground state of a Bose system of any density should correspond to a liquid or gas, but not to a crystal. The main point is that any anisotropic state of a system of spinless bosons is degenerate. We prove this for an infinite three-dimensional (3D) system and a finite ball-shaped 3D system. One can expect that it is true also for a finite system of any form. Therefore, the anisotropic state cannot be the genuine ground state. Hence, a zero-temperature natural 3D crystal should correspond to an excited state of a Bose system. The wave function $\Psi^{c}_{0}$ of a zero-temperature 3D Bose crystal is proposed for zero boundary conditions. Apparently, such $\Psi^{c}_{0}$ corresponds to a local minimum of energy (absolute minimum corresponds to a liquid). Those properties yield the possibility of existence of superfluid liquid H$_{2}$, Ne, Ar, and other inert elements. We propose several possible experimental ways of obtaining them.