Soft Quantum Lattice Gas and the Existence of a Supersolid

Abstract

We propose a soft quantum lattice model for liquid and solid ⁴He at 0 K. Our model is capable of representing a compressible solid. Transfer matrix elements to cause O.D.L.R.O and effective repulsive interaction between atoms are assumed to depend on the lattice parameter a with two model parameters p and q as exponents of the “a” dependence of transfer matrix elements and effective repulsive interaction, respectively. We find that they are restricted to 0<p<3, 4.2<q<5 in order to account for the super fluid-normal solid phase change by our model. We examine the possibility of the coexistence of O.D.L.R.O and D.L.R.O (supersolid phase). We find that by our model the supersolid phase is possible when q<4.2, p=2.