Matrix-Product Ansatz for Excited States of Fractional Quantum Hall Systems

TL;DR

This paper develops an analytical method using matrix-product states to calculate excitation spectra in fractional quantum Hall systems, revealing magneto-roton behavior.

Contribution

It introduces a novel variational approach for excited states in fractional quantum Hall systems using matrix-product formalism.

Findings

Analytical calculation of excitation spectra

Identification of magneto-roton behavior

Effective variational wave functions for excitations

Abstract

Recently, it was discussed that the $\nu=1/3$ fractional quantum Hall state can be expressed by a one-dimensional lattice model with an exact matrix-prduct ground state, when toroidal boundary conditions are assumed for a narrow strip [Phys. Rev. Lett. {\bf 109} (2012) 016401]. In this article, we discuss how the excitation spectra of this system are calculated analytically based on the matrix-product formalism. We introduce variational wave functions for various momenta and optimize them. The obtained spectra of the charge neutral excitations show the magneto-roton behavior.