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

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.

4 pages, 1 figure. Proceedings of nanoPHYS'12 held in Tokyo on Dec.17-19 (JPSJ Supplement)

References in corpus (5)

• Half-Filled Lowest Landau Level on a Thin Torus
• Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect
• Exactly Solvable Fermion Chain Describing a $\nu =1/3$ Fractional Quantum Hall State
• Spin-chain description of fractional quantum Hall states in the Jain series
• Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation

Cited by in corpus (3)

• Spectral Gaps and Incompressibility in a $\nu =1/3$ Fractional Quantum Hall System
• The spectral gap of a fractional quantum Hall system on a thin torus
• On a bulk gap strategy for quantum lattice models