Fermionic and bosonic Laughlin state on thick cylinders

TL;DR

This paper analyzes the Laughlin wave function for particles on a thick cylinder, demonstrating the existence of a unique limiting correlation structure with a non-trivial period, applicable to both fermions and bosons.

Contribution

It establishes the convergence of correlation functions to a unique limit state with periodicity, and connects algebraic structures to ground state perturbations and quantum spin chain analogies.

Findings

Correlation functions have a unique limit in the many-particle regime.

The limit state exhibits a non-trivial axial periodicity.

The monomer-dimer function is an exact ground state of a finite-range Hamiltonian.

Abstract

We investigate a many-body wave function for particles on a cylinder known as Laughlin's function. It is the power of a Vandermonde determinant times a Gaussian. Our main result is: in a many-particle limit, at fixed radius, all correlation functions have a unique limit, and the limit state has a non-trivial period in the axial direction. The result holds regardless how large the radius is, for fermions as well as bosons. In addition, we explain how the algebraic structure used in proofs relates to a ground state perturbation series and to quasi-state decompositions, and we show that the monomer-dimer function introduced in an earlier work is an exact, zero energy, ground state of a suitable finite range Hamiltonian; this is interesting because of formal analogies with some quantum spin chains.