## Abstract

The model Hamiltonian of a two-dimensional Bose liquid (proposed earlier by Kane et al. as the Hamiltonian which has Jastrow-type wavefunctions Ψ_{0}{r_{i}} α ∏_{j>k} |r_{j} - r_{k}|^{2α} as the ground-state solution), is shown to possess non-relativistic 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 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 q) spectrum of single-particle excitations beyond the superfluid ground state (realized at low α's). The ground state Ψ_{0} 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 scenario's of the ground-state phase transitions as a function of α are discussed.

Original language | English |
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Pages (from-to) | 665-684 |

Number of pages | 20 |

Journal | Nuclear Physics B |

Volume | 506 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Dec 1997 |

Externally published | Yes |

## Keywords

- Matrix models
- Non-relativistic supersymmetry
- Superfluidity