Supersymmetric model of a 2D long-range Bose liquid

M. V. Feigel'man, M. A. Skvortsov

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10 Citations (Scopus)

Abstract

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} α ∏j>k |rj - rk| 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 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 scenario's of the ground-state phase transitions as a function of α are discussed.

Original languageEnglish
Pages (from-to)665-684
Number of pages20
JournalNuclear Physics B
Volume506
Issue number3
DOIs
Publication statusPublished - 1 Dec 1997
Externally publishedYes

Keywords

  • Matrix models
  • Non-relativistic supersymmetry
  • Superfluidity

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