scholarly journals Holomorphicity, vortex attachment, gauge invariance and the fractional quantum hall effect

2021 ◽  
Author(s):  
ABHISHEK AGARWAL
Keyword(s):  
Mean Field Theory ◽  
Quantum Hall ◽  
Mean Field ◽  
Spherical Geometry ◽  
Field Approximation ◽  
Wave Functions ◽  
Mean Field Approximation ◽  
Exact Results ◽  
Gauge Invariant ◽  
Fractional Quantum Hall

Abstract A gauge invariant reformulation of nonrelativistic fermions in background magnetic fields is used to obtain the Laughlin and Jain wave functions as exact results in Mean Field Theory (MFT). The gauge invariant framework trades the U(1) gauge symmetry for an emergent holomorphic symmetry and fluxes for vortices. The novel holomorphic invariance is used to develop an analytical method for attaching vortices to particles. Vortex attachment methods introduced in this paper are subsequently employed to construct the Read operator within a second quantized framework and obtain the Laughlin and Jain wave functions as exact results entirely within a mean-field approximation. The gauge invariant framework and vortex attachment techniques are generalized to the case of spherical geometry and spherical counterparts of Laughlin and Jain wave functions are also obtained exactly within MFT.

MEAN-FIELD THEORY FOR LAYERED HIGH-TEMPERATURE SUPERCONDUCTORS

1988 ◽  
Vol 02 (05) ◽  
pp. 1059-1065 ◽  
Author(s):  
D. Baeriswyl ◽  
T. Schneider
Keyword(s):  
High Temperature Superconductors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Interlayer Coupling ◽  
Interlayer Spacing ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Pairing Mechanism ◽  
The Mean

Using the mean-field approximation we study a model for quasi-two-dimensional layered superconductors. The interlayer coupling, assumed to be mediated by a small electron hopping term, is found to leave Tc practically unaffected. Consequently, a three-dimensional pairing mechanism is required to explain the observed dependence of Tc on the average interlayer spacing in the Bi and Tl compounds.

scholarly journals Calculation of the Static Properties of Local Moment Systems by the Mean Field Method

1975 ◽  
Vol 28 (6) ◽  
pp. 685 ◽  
Author(s):  
AM Stewart
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Field Method ◽  
Local Moment ◽  
Mean Field Approximation ◽  
Static Properties ◽  
The Past ◽  
The Mean

It is demonstrated that two different methods which have been used in the past to calculate the static properties oflocal moment systems in the mean field approximation are incomplete. A proof is given of the correctness of another method that the author has used in several previous calculations. It is found that some exact and very general relationships exist between the conduction electron magnetization and the local moment magnetization even when it is not valid to treat the interactions between the magnetic atoms by mean field theory.

scholarly journals THE CJT CALCULATION IN STUDYING NUCLEAR MATTER BEYOND MEAN FIELD APPROXIMATION

2008 ◽  
Vol 23 (21) ◽  
pp. 1769-1780 ◽  
Author(s):  
SONG SHU ◽  
JIA-RONG LI
Keyword(s):  
Field Theory ◽  
Nuclear Matter ◽  
Chemical Potential ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Medium Effects ◽  
Effective Masses ◽  
Walecka Model

We have introduced the Cornwall–Jackiw–Tomboulis (CJT) resummation scheme in studying nuclear matter. Based on the CJT formalism and using Walecka model, we have derived a set of coupled Dyson equations of nucleons and mesons. Neglecting the medium effects of the mesons, the usual mean field theory (MFT) results can be obtained. The beyond MFT calculations have been performed by thermodynamic consistently determining the meson effective masses and solving the coupled gap equations for nucleons and mesons together. The numerical results for the nucleon and meson effective masses at finite temperature and chemical potential in nuclear matter are discussed.

ON THE VALIDITY OF MEAN-FIELD THEORY FOR ANYONS ON A LATTICE

1992 ◽  
Vol 06 (30) ◽  
pp. 1951-1960 ◽  
Author(s):  
A.A. OVCHINNIKOV ◽  
An. A. OVCHINNIKOV
Keyword(s):  
Large Deviation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Hard Core ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Phase Fluctuations ◽  
Fermi Statistics ◽  
The Mean ◽  
Field Approaches

We examine the validity of the mean-field approximation for anyons on a lattice at high density. The phase fluctuations for a large deviation from the Fermi statistics, in particular for the hard core bosons, are shown to be large. The importance of the phase fluctuations in different fermionic mean-field approaches for the antiferromagnetic Heisenberg model is stressed.

CAR-ORIENTED MEAN-FIELD THEORY REVISITED

2004 ◽  
Vol 18 (17) ◽  
pp. 887-894 ◽  
Author(s):  
YU-FUNG CHIEN ◽  
DING-WEI HUANG
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Critical Density ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Stochastic Noise ◽  
Collective Effect ◽  
Self Consistent ◽  
The Mean

We study the Car-Oriented Mean-Field approximation (COMF) to the Nagel–Schreckenberg model in the case of v max =3. The self-consistent equations are obtained. The solution is reached by the method of iteration. When the stochastic noise is small, the numerical simulations can be well described by the mean-field theory. When the stochastic noise is large, the flux around critical density is overestimated. The overshooting of the free flow can be attributed to the collective effect of the stochastic noise.

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