Using exact numerical diagonalization we have studied correlated many-electron ground states in a partially filled second Landau level.We consider filling fractions ν = 1/2 and 2/5, for which incompressible quantum liquids with non-Abelian anion statistics have been proposed.Our calculations include finite layer width, Landau level mixing and arbitrary deformation of the interaction pseudopotential.Computed energies, gaps, and correlation functions support the non-Abelian ground states at both ν = 1/2 ("Pfaffian") and ν = 2/5 ("parafermion" state).Using exact numerical diagonalization we have studied correlated many-electron ground states in a partially filled second Landau level.We consider filling fractions ν = 1/2 and 2/5, for which incompressible quantum liquids with non-Abelian anion statistics have been proposed.Our calculations include finite layer width, Landau level mixing and arbitrary deformation of the interaction pseudopotential.Computed energies, gaps, and correlation functions support the non-Abelian ground states at both ν = 1/2 ("Pfaffian") and ν = 2/5 ("parafermion" state).

Acta Physica Polonica ANov 1, 20090 citations

Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux

Lachezar S. Georgiev

Using the effective conformal field theory for the quantum Hall edge states we propose a compact and convenient scheme for the computation of the periods, amplitudes, and temperature behavior of the chiral persistent currents and the magnetic susceptibilities in the mesoscopic disk version of the ${Z}_{k}$ parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov--Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a nontrivial contribution coming from the neutral sector. We emphasize the crucial role of the nonholomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.Using the effective conformal field theory for the quantum Hall edge states we propose a compact and convenient scheme for the computation of the periods, amplitudes, and temperature behavior of the chiral persistent currents and the magnetic susceptibilities in the mesoscopic disk version of the ${Z}_{k}$ parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov--Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a nontrivial contribution coming from the neutral sector. We emphasize the crucial role of the nonholomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.

arXiv:cond-mat/0311339Physical Review BFeb 13, 20047 citations

Instability of a state of a quantum Hall effect in 2D spin systems

Sergei Khlebnikov

Jan 1, 19910 citations

Spin–Orbit Interaction Enhanced Fractional Quantum Hall States in the Second Landau Level

Toru Ito, Kentaro Nomura, Naokazu Shibata

We study the fractional quantum Hall effect at filling fractions 7/3 and 5/2 in the presence of the spin-orbit interaction, using the exact diagonalization method and the density matrix renormalization group (DMRG) method in a spherical geometry. Trial wave functions at these fillings are the Laughlin state and the Moore-Reed-Pfaffian state. The ground state excitation energy gaps and pair-correlation functions at fractional filling factor 7/3 and 5/2 in the second Landau level are calculated. We find that the spin-orbit interaction stabilizes the fractional quantum Hall states.We study the fractional quantum Hall effect at filling fractions 7/3 and 5/2 in the presence of the spin-orbit interaction, using the exact diagonalization method and the density matrix renormalization group (DMRG) method in a spherical geometry. Trial wave functions at these fillings are the Laughlin state and the Moore-Reed-Pfaffian state. The ground state excitation energy gaps and pair-correlation functions at fractional filling factor 7/3 and 5/2 in the second Landau level are calculated. We find that the spin-orbit interaction stabilizes the fractional quantum Hall states.

arXiv:1005.1446Journal of the Physical Society of JapanJul 15, 20104 citations

Quantum Hall Gas around Half-filled Landau Level

展希前田, 哲行落合, 健三石川

素粒子論研究May 20, 19990 citations

{Z}_{k}

parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov--Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a nontrivial contribution coming from the neutral sector. We emphasize the crucial role of the nonholomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.