Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1997-03-25
Nucl. Phys. B 506 [FS], 665 (1997)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
Revtex; 12 pages, 1 Postscript figure
Scientific paper
10.1016/S0550-3213(97)00616-0
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 $\alpha=1/2$ 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 $\alpha$, 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 $\alpha$'s). The ground-state at very large $\alpha$ 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 $\alpha$ are discussed.
Feigel'man Michael V.
Skvortsov Mikhail A.
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