Soluble `Supersymmetric' Quantum XY Model

TL;DR

This paper introduces a supersymmetric quantum rotor model with an exactly solvable ground state, exhibiting a vortex-binding transition that alters the universality class and features a metallic phase with algebraic order but zero superfluid density.

Contribution

It presents a novel supersymmetric modification of the quantum rotor model with an exactly solvable ground state and analyzes its phase transition and properties.

Findings

The model undergoes a vortex-binding transition from insulator to metal.

The transition's universality class changes due to relevant three-site terms.

The metallic phase exhibits algebraic off-diagonal long-range order with zero superfluid density.

Abstract

We present a `supersymmetric' modification of the $d$-dimensional quantum rotor model whose ground state is exactly soluble. The model undergoes a vortex-binding transition from insulator to metal as the rotor coupling is varied. The Hamiltonian contains three-site terms which are relevant: they change the universality class of the transition from that of the ($d+1$)--- to the $d$-dimensional classical XY model. The metallic phase has algebraic ODLRO but the superfluid density is identically zero. Variational wave functions for single-particle and collective excitations are presented.