Exact microscopic wave function for a topological quantum membrane

TL;DR

This paper introduces an exact microscopic ground state wave function for a topological quantum membrane in a higher-dimensional quantum Hall system, providing a non-perturbative quantization method for topological membranes.

Contribution

It presents the first exact ground state wave function for a topological quantum membrane and develops a non-perturbative quantization approach using non-commutative algebra.

Findings

Exact ground state wave function for a topological membrane

Construction of variational excited state wave functions

Introduction of a non-perturbative quantization method

Abstract

The higher dimensional quantum Hall liquid constructed recently supports stable topological membrane excitations. Here we introduce a microscopic interacting Hamiltonian and present its exact ground state wave function. We show that this microscopic ground state wave function describes a topological quantum membrane. We also construct variational wave functions for excited states using the non-commutative algebra on the four sphere. Our approach introduces a non-perturbative method to quantize topological membranes.