Supersymmetric Model of a 2D Long-Range Bose Liquid

TL;DR

This paper reveals a supersymmetric structure in a 2D Bose liquid model, links it to random matrix theory at a specific coupling, and explores its excitation spectrum and phase transitions.

Contribution

It demonstrates nonrelativistic supersymmetry in a 2D Bose liquid model and establishes exact relations for correlation functions and excitation spectra.

Findings

Supersymmetry is present at a specific coupling constant.

At $eta=1/2$, the model maps to Gaussian complex matrix eigenvalues.

The excitation spectrum is derived for low wavevectors.

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 $\alpha=1/2$ 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.