Supersymmetric model of a 2D long-range Bose liquid Original Research Article

The model Hamiltonian of a two-dimensional Bose liquid (proposed earlier by Kane et al. as the Hamiltonian which has Jastrow-type wavefunctions ψ0{ri} ∝ Πj>k|rj−rk|2α a ground-state solution), is shown to possess non-relativistic supersymmetry. For the special value of the coupling constant α = 12 the quantum mechanics described by this Hamiltonian is shown to be equivalent to the dynamics of (complex) eigenvalues of a random Gaussian ensemble of normal complex matrices. For general α, an exact relation between the equal-time current-current and density-density correlation functions is obtained, and used to derive an asymptotically exact (at low wavevectors θ) spectrum of single-particle excitations beyond the superfluid ground state (realized at low αʹs). The ground state ψ0 at very large α is shown to be of “quantum hexatic” type, possessing long-range orientational order and quasi-long-range translational order but with zero shear modulus. Possible scenarioʹs of the ground-state phase transitions as a function of α are discussed.