scholarly journals ANISOTROPY IN THE COMPRESSIBLE QUANTUM HALL STATE

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1373-1376
Author(s):  
NOBUKI MAEDA
Keyword(s):  
Mean Field Theory ◽  
Density Wave ◽  
Quantum Hall ◽  
Mean Field ◽  
Dimensional System ◽  
Von Neumann ◽  
One Dimensional ◽  
Hartree Fock ◽  
Fermion Systems ◽  
Lattice Fermion

Using a mean field theory on the von Neumann lattice, we study compressible anisotropic states around ν=l+1/2 in the quantum Hall system. The Hartree-Fock energy of the unidirectional charge density wave (UCDW) are calculated self-consistently. In these states the UCDW seems to be the most plausible state. We show that the UCDW is regarded as a collection of the one-dimensional lattice fermion systems which extend to the uniform direction. The kinetic energy of this one-dimensional system is induced from the Coulomb interaction term and the self-consistent Fermi surface is obtained.

scholarly journals ANDERSON LOCALIZATION VS. MOTT–HUBBARD METAL–INSULATOR TRANSITION IN DISORDERED, INTERACTING LATTICE FERMION SYSTEMS

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1727-1755 ◽  
Author(s):  
Krzysztof Byczuk ◽  
Walter Hofstetter ◽  
Dieter Vollhardt
Keyword(s):  
Anderson Localization ◽  
Mean Field Theory ◽  
Mean Field ◽  
Antiferromagnetic Order ◽  
Strongly Correlated ◽  
Theoretical Understanding ◽  
Particle Correlation ◽  
Fermion Systems ◽  
Disordered Lattice ◽  
Lattice Fermion

We review recent progress in our theoretical understanding of strongly correlated fermion systems in the presence of disorder. Results were obtained by the application of a powerful nonperturbative approach, the dynamical mean-field theory (DMFT), to interacting disordered lattice fermions. In particular, we demonstrate that DMFT combined with geometric averaging over disorder can capture Anderson localization and Mott insulating phases on the level of one-particle correlation functions. Results are presented for the ground state phase diagram of the Anderson–Hubbard model at half-filling, both in the paramagnetic phase and in the presence of antiferromagnetic order. We find a new antiferromagnetic metal which is stabilized by disorder. Possible realizations of these quantum phases with ultracold fermions in optical lattices are discussed.

Ferromagnetism, Dimerization, Charge and Spin Density Waves in Quasi-One-Dimensional Organic Polymers: Self-Consistent Mean Field Theory

1998 ◽  
Vol 12 (20) ◽  
pp. 2031-2044 ◽  
Author(s):  
Shi-Dong Liang ◽  
Qianghua Wang ◽  
Z. D. Wang ◽  
Shun-Qing Shen
Keyword(s):  
Field Theory ◽  
Charge Density ◽  
Spin Density ◽  
Charge Density Wave ◽  
Mean Field Theory ◽  
Density Wave ◽  
Mean Field ◽  
One Dimensional ◽  
Ferromagnetic Order ◽  
Self Consistent

We address the low temperature properties of quasi-one-dimensional organic polymers, which may be described by a modified Anderson lattice-Su–Schrieffer–Heeger Hamiltonian. The condition and nature of various orders, such as, the ferromagnetic order, the dimerization order, the charge density wave order and the spin density wave order, are analyzed by a self-consistent mean field theory. Analytical results are obtained for a specific case. The topological structure of the chain leads to a flatband structure of the energy band, which gives rise to a ferromagnetic order in the case of half filling at low temperatures. The on-site Coulomb repulsion enhances the ferromagnetic order, while the nearest-neighbor interaction (V) suppresses both the ferromagnetic order and the dimerization, and leads to the charge density wave. The π–d hybridization (td) suppresses the dimerization, and does not affect the magnetization. The ferromagnetic order and dimerization order coexist for weak td.

Symmetry Violations in Partially Oxidized One-Dimensional (1D)Transition Metal Polymers. Metal-Ligand-Metal(M-L-M) Bridged Systems

1984 ◽  
Vol 39 (9) ◽  
pp. 807-829
Author(s):  
Michael C. Böhm
Keyword(s):  
Transition Metal ◽  
Density Wave ◽  
Tight Binding ◽  
Mean Field ◽  
Valence Bond ◽  
Hole State ◽  
One Dimensional ◽  
Metal Derivatives ◽  
A Charge ◽  
Metal Ligand

The band structure of the metal-ligand-metal (M-L-M) bridged quasi one-dimensional (1D) cyclopentadienylmanganese polymer, MnCp 1, has been studied in the unoxidized state and in a partly oxidized modification with one electron removed from each second MnCp fragment. The tight-binding approach is based on a semiempirical self-consistent-field (SCF) Hartree-Fock (HF) crystal orbital (CO) model of the INDO-type (intermediate neglect of differential overlap) combined with a statistical averaging procedure which has its origin in the grand canonical ensemble. The latter approximation allows for an efficient investigation of violations of the translation symmetries in the oxidized 1D material. The oxidation process in 1 is both ligand- and metal-centered (Mn 3d-2 states). The mean-field minimum corresponds to a charge density wave (CDW) solution with inequivalent Mn sites within the employed repeat-units. The symmetry adapted solution with electronically identical 3d centers is a maximum in the variational space. The coupling of this electronic instability to geometrical deformations is also analyzed. The ligand amplitudes encountered in the hole-state wave function prevent extremely large charge separations between the 3d centers which are found in ID systems without bridging moieties (e.g. Ni(CN)2-5 chain). The symmetry reduction in oxidized 1 is compared with violations of spatial symmetries in finite transition metal derivatives and simple solids. The stabilization of the valence bond-type (VB) solution is physically rationalized (i.e. left-right correlations between the 3d centers). The computational results derived for 1 are generalized to oxidized transition metal chains with band occupancies that are simple fractions of the number of stacking units and to 1D systems that deviate from this relation. The entropy-influence for temperatures T ≠ 0 is shortly discussed (stabilization of domain or cluster structures).

scholarly journals RELATIVE MOTION CORRECTION TO FISSION BARRIERS

2008 ◽  
Vol 17 (01) ◽  
pp. 151-159 ◽  
Author(s):  
J. SKALSKI
Keyword(s):  
Relative Motion ◽  
Cluster Model ◽  
Motion Correction ◽  
Mean Field Theory ◽  
Mean Field ◽  
Ternary Fission ◽  
Skyrme Interaction ◽  
Hartree Fock ◽  
Fission Barriers ◽  
The Mean

We discuss the effect of kinetic energy of the relative motion becoming spurious for separate fragments on the selfconsistent mean-field fission barriers. The treatment of the relative motion in the cluster model is contrasted with the necessity of a simpler and approximate approach in the mean-field theory. A scheme of the energy correction to the Hartree-Fock is proposed. The results obtained with the effective Skyrme interaction SLy 6 show that the correction, previously estimated as ~ 8 MeV in A = 70 - 100 nuclei, amounts to 4 MeV in the medium heavy nucleus 198 Hg and to null in 238 U . However, the corrected barrier implies a shorter fission half-life of the latter nucleus. The same effect is expected to lower barriers for multipartition (i.e. ternary fission, etc) and make hyperdeformed minima less stable.

CHARGE-FLUX DENSITY WAVES: ANYONS IN A PERIODIC POTENTIAL

1991 ◽  
Vol 05 (21) ◽  
pp. 1431-1438
Author(s):  
D. M. Gaitonde ◽  
Sumathi Rao
Keyword(s):  
Flux Density ◽  
Periodic Potential ◽  
Mean Field Theory ◽  
Density Wave ◽  
Mean Field ◽  
Landau Levels ◽  
Filling Fraction ◽  
Lattice Periodicity ◽  
Magnetic Length ◽  
A Charge

We show that the lattice periodicity which causes a modulation of the charge density by a wave vector q also leads to a modulation of the flux density if the charged particles are anyons. Within mean field theory, we obtain a charge and flux density wave (CFDW) where the degenerate Landau levels of a constant magnetic field split into bands. For a weak periodic flux superimposed on a strong constant flux, anyon superconductivity at integer filling of Landau levels (corresponding to a statistics parameter of θ = π(1 − 1/ν) with ν = n = integer ) is not affected. However, at statistics corresponding to non-integer filling of Landau levels, for certain commensurability conditions between the lattice length (a), the magnetic length (l) and the filling fraction (ν), gaps open up at the Fermi level and convert an anyon metal into an anyon insulator.

scholarly journals A one-dimensional modified TASEP model on a track of variable length: analytical and computational results

2021 ◽  
Vol 2090 (1) ◽  
pp. 012025
Author(s):  
B. Reed ◽  
E. Aldrich ◽  
L. Stoleriu ◽  
D.A. Mazilu ◽  
I. Mazilu
Keyword(s):  
Monte Carlo ◽  
Molecular Motors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Limited Range ◽  
Field Methods ◽  
One Dimensional ◽  
Emergent Features ◽  
Simulation Results ◽  
Mean Field Methods

Abstract We present analytical solutions and Monte Carlo simulation results for a one-dimensional modified TASEP model inspired by the interplay between molecular motors and their cellular tracks of variable lengths, known as microtubules. Our TASEP model incorporates rules for changes in the length of the track based on the occupation of the first two sites. Using mean-field theory, we derive analytical results for the particle densities and particle currents and compare them with Monte Carlo simulations. These results show the limited range of mean-field methods for models with localized high correlation between particles. The variability in length adds to the complexity of the model, leading to emergent features for the evolution of particle densities and particle currents compared to the traditional TASEP model.

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