Toward a new theory of the fractional quantum Hall effect: The many-body spectra and energy gaps at $\nu<1$

• URL: http://arxiv.org/abs/2306.14931v1
• Date: Sun, 25 Jun 2023 22:40:03 GMT
• Title: Toward a new theory of the fractional quantum Hall effect: The many-body spectra and energy gaps at $\nu<1$
• Authors: S. A. Mikhailov
• Abstract summary: In this paper I continue to study exact properties of a small ($Nle 7$) system of two-dimensional electrons lying on the lowest Landau level. The physical mechanisms of the appearance of energy gaps in many-particle electron spectra are elucidated.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a recent paper (arXiv:2206.05152v4), using the exact diagonalization technique, I calculated the energy and other physical properties (electron density, pair correlation function) of a system of $N\le 7$ two-dimensional electrons at the Landau level filling factor $\nu=1/3$, and showed that the variational many-body wave function proposed for this filling factor by Laughlin is far from the true ground state. In this paper I continue to study exact properties of a small ($N\le 7$) system of two-dimensional electrons lying on the lowest Landau level. I analyze the energies and electron densities of the systems with $N\le 7$ electrons continuously as a function of the magnetic field in the range $1/4\lesssim\nu<1$. The physical mechanisms of the appearance of energy gaps in many-particle electron spectra are elucidated. The results obtained clarify the true nature of the ground and excited states of the considered systems.

Related papers

• Distinguishing erbium dopants in Y$_2$O$_3$ by site symmetry: \textit{ ab initio} theory of two spin-photon interfaces [0.0]
  We present a first-principles study of defect formation and electronic structure of erbium (Er)-doped yttria (Y$ $4$O$_3$) This is an emerging material for spin-photon interfaces in quantum information science due to the narrow linewidth optical emission from Er dopants. We calculate formation energies of neutral, negatively, and positively charged Er dopants and find the charge neutral configuration to be the most stable.
  arXiv  Detail & Related papers  (2023-05-25T16:42:27Z)
• Foldy-Wouthuysen transformation and multiwave states of a graphene electron in external fields and free (2+1)-space [91.3755431537592]
  Graphene electrons in a static electric field can exist in the multiwave Hermite-Gauss states defining non-spreading coherent beams. It is proven that the Hermite-Gauss beams exist even in the free space.
  arXiv  Detail & Related papers  (2023-05-07T17:03:00Z)
• Self-trapping of slow electrons in the energy domain [0.0]
  We show that slow electrons are subject to strong confinement in the energy domain due to the non-vanishing curvature of the electron dispersion. The spectral trap is tunable and an appropriate choice of light field parameters can reduce the interaction dynamics to only two energy states.
  arXiv  Detail & Related papers  (2022-09-29T15:07:11Z)
• Spin Current Density Functional Theory of the Quantum Spin-Hall Phase [59.50307752165016]
  We apply the spin current density functional theory to the quantum spin-Hall phase. We show that the explicit account of spin currents in the electron-electron potential of the SCDFT is key to the appearance of a Dirac cone.
  arXiv  Detail & Related papers  (2022-08-29T20:46:26Z)
• Valleytronic full configuration-interaction approach: An application to the excitation spectra of Si double-dot qubits [0.0]
  We study the influence of strong electron-electron interactions and Wigner-molecule (WM) formation on the spectra of Si qubits. We present results for both the $E_rm ST E_V$ and $E_rm ST E_V$ cases.
  arXiv  Detail & Related papers  (2022-08-11T03:55:52Z)
• Computational Insights into Electronic Excitations, Spin-Orbit Coupling Effects, and Spin Decoherence in Cr(IV)-based Molecular Qubits [63.18666008322476]
  We provide insights into key properties of Cr(IV)-based molecules aimed at assisting chemical design of efficient molecular qubits. We find that the sign of the uniaxial zero-field splitting (ZFS) parameter is negative for all considered molecules. We quantify (super)hyperfine coupling to the $53$Cr nuclear spin and to the $13C and $1H nuclear spins.
  arXiv  Detail & Related papers  (2022-05-01T01:23:10Z)
• $\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited vibrational state [77.34726150561087]
  Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-15T17:08:33Z)
• Four-Dimensional Scaling of Dipole Polarizability in Quantum Systems [55.54838930242243]
  Polarizability is a key response property of physical and chemical systems. We show that polarizability follows a universal four-dimensional scaling law. This formula is also applicable to many-particle systems.
  arXiv  Detail & Related papers  (2020-10-22T15:42:36Z)
• Theoretical investigation of the Freeman resonance in the dissociative ionization of $H_2+$ [0.0]
  The dissociative ionization of $H+$ in linearly polarized, 400 nm laser pulses is simulated by solving a three-particle time-dependent Schr"odinger equation in full dimensionality. The analysis of the wavefunction for electrons and protons after the pulse are presented, where we find $U_p$ is absorbed by the Freeman resonances between two excited ungerade states.
  arXiv  Detail & Related papers  (2020-08-21T15:10:48Z)
• Electrically tuned hyperfine spectrum in neutral Tb(II)(Cp$^{\rm{iPr5}}$)$_2$ single-molecule magnet [64.10537606150362]
  Both molecular electronic and nuclear spin levels can be used as qubits. In solid state systems with dopants, an electric field was shown to effectively change the spacing between the nuclear spin qubit levels. This hyperfine Stark effect may be useful for applications of molecular nuclear spins for quantum computing.
  arXiv  Detail & Related papers  (2020-07-31T01:48:57Z)
• Ab initio properties of the NaLi molecule in the $a^3\Sigma^+$ electronic state [0.0]
  We calculate the electronic and rovibrational structure of ultracold polar and magnetic molecules with spectroscopic accuracy. We show that quantum chemistry methods are capable of predicting scattering properties of manyelectron systems.
  arXiv  Detail & Related papers  (2020-03-26T17:39:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.