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Supersymmetric Model of a 2D Long-Range Bose Liquid

M. V. Feigel'man·M. A. Skvortsov
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Abstract

The model Hamiltonian of a two-dimensional Bose liquid (proposed earlier by Kane, Kivelson, Lee and Zhang as the Hamiltonian which has Jastrow-type wavefunctions as the ground-state solution), is shown to possess nonrelativistic supersymmetry. For the special value of the coupling constant $α=1/2$ the quantum mechanics described by this Hamiltonian is shown to be equivalent to the dynamics of (complex) eigenvalues of 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 q) spectrum of single-particle excitations beyond the superfluid ground-state (realized at low $α$'s). The ground-state 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 scenaria of the ground-state phase transitions as function of $α$ are discussed.

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M. V. Feigel'man, M. A. Skvortsov. 1997-03-25. Supersymmetric Model of a 2D Long-Range Bose Liquid. https://doi.org/10.1016/s0550-3213(97)00616-0

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