Renormalizationgroup analysis of the groundstate properties of dilute Bose systems in d spatial dimensions
Abstract
A lowdensity system of Bose particles of mass m and density n interacting through a shortrange potential with range a is considered in d dimensions using a renormalization approach. The expansion parameter of the groundstate energy E per particle for d<2 is (na^{d})^{(2d)/d}. For some special cases the leading universal term of the expansion E=C_{d}ħ^{2}n^{2/d}/m+..., where C_{d} is a universal number, gives an exact expression for the groundstate energy. For d>2 the energy expansion scales as E=(1/2)nt[1+const(nf^{d})^{(d2)/2}], where t is the pseudopotential connected to the bare potential and f is the corresponding scattering length. This is a generalization of the generally accepted results (for d=3) of Lee and Yang [Phys. Rev. 105, 1119 (1957)], but a stronger condition for validity is found: nf^{d}<<(f/a)^{2}<=1. The possibility of the formation of quantum crystal phases is considered. We argue that for d<2, crystal phases and melting transitions in the traditional sense are impossible. For d>2 the liquid phase is stable relative to the solid one. The corresponding energy difference diminishes for d>2+0, and for d=2 it is much less than was suggested by Nelson [J. Stat. Phys. 57, 511 (1989)]; here the liquid phase is stable only in the extremely dilute regime. For d>2, attractive Bose systems exhibit a secondorder phase transition connected to the formation of the bound state. For d<=2 only the bound state can occur.
 Publication:

Physical Review B
 Pub Date:
 November 1992
 DOI:
 10.1103/PhysRevB.46.11749
 Bibcode:
 1992PhRvB..4611749K
 Keywords:

 74.20.De;
 74.30.Gn;
 74.60.Ge;
 74.30.Ci;
 Phenomenological theories