scholarly journals COLLECTIVE COORDINATE ACTION FOR CHARGED SIGMA-MODEL VORTICES IN FINITE GEOMETRIES

1993 ◽  
Vol 08 (19) ◽  
pp. 1815-1820 ◽  
Author(s):  
THEODORE J. ALLEN
Keyword(s):  
Sigma Model ◽  
Quantum Hall ◽  
Finite Size ◽  
Effective Field ◽  
Finite Geometries ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Collective Coordinate ◽  
The Green Function ◽  
Laughlin Wave Function

We apply the method of Lund to formulate a variational principle for the motion of charged vortices in an effective nonlinear Schrödinger field theory describing finite size two-dimensional quantum Hall samples under the influence of an arbitrary perpendicular magnetic field. Freezing out variations in the modulus of the effective field yields a U(1) sigma-model. A duality transformation on the sigma-model reduces the problem to finding the Green function for a related electrostatics problem. This duality connects the plasma analogy to the Laughlin wave function directly to a vortex gas description of the fractional quantum Hall effect.

Entanglement entropy of fractional quantum Hall systems with short range disorder

2015 ◽  
Vol 29 (12) ◽  
pp. 1550065 ◽  
Author(s):  
B. A. Friedman ◽  
G. C. Levine
Keyword(s):  
Short Range ◽  
Entanglement Entropy ◽  
Quantum Hall ◽  
Finite Size ◽  
Disorder Strength ◽  
Fractional Quantum ◽  
Finite Size Effects ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Liquid Transition

The critical value of the mobility for which the ν = 5/2 quantum Hall effect is destroyed by short range disorder is determined from an earlier calculation of the entanglement entropy. The value μ = 2.0 ×106 cm 2/ Vs agrees well with experiment. This agreement is particularly significant in that there are no adjustable parameters. Entanglement entropy versus disorder strength for ν = 1/2, ν = 9/2 and ν = 7/3 is calculated. For ν = 1/2 there is no evidence for a transition for the disorder strengths considered; for ν = 9/2 there appears to be a stripe-liquid transition. For ν = 7/3 there again appears to be a transition at similar value of the disorder strength as the ν = 5/2 transition but there are stronger finite size effects.

scholarly journals Automatic design of Hamiltonians

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 315
Author(s):  
Kiryl Pakrouski
Keyword(s):  
Optimization Problem ◽  
Quantum Hall ◽  
Finite Size ◽  
Universality Class ◽  
Test System ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Interaction Terms ◽  
The Given ◽  
Hamiltonian Properties

We formulate an optimization problem of Hamiltonian design based on the variational principle. Given a variational ansatz for a Hamiltonian we construct a loss function to be minimised as a weighted sum of relevant Hamiltonian properties specifying thereby the search query. Using fractional quantum Hall effect as a test system we illustrate how the framework can be used to determine a generating Hamiltonian of a finite-size model wavefunction (Moore-Read Pfaffian and Read-Rezayi states), find optimal conditions for an experiment or "extrapolate" given wavefunctions in a certain universality class from smaller to larger system sizes. We also discuss how the search for approximate generating Hamiltonians may be used to find simpler and more realistic models implementing the given exotic phase of matter by experimentally accessible interaction terms.

scholarly journals CHERN–SIMONS THEORY OF FRACTIONAL QUANTUM HALL EFFECT IN (PSEUDO) MASSLESS DIRAC ELECTRONS

2011 ◽  
Vol 25 (20) ◽  
pp. 2779-2785
Author(s):  
HUABI ZENG
Keyword(s):  
Quantum Hall ◽  
Effective Field ◽  
Simons Theory ◽  
Arbitrary Integer ◽  
Fractional Quantum ◽  
Hall Conductance ◽  
Fractional Quantum Hall ◽  
Topological Excitations ◽  
Chern Simons ◽  
Chern Simons Theory

We derive the effective-field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be σxy=e2/h(2k-1) where k is arbitrary integer. There are also topological excitations which have fractional charge and obey fractional statistics.

ON TOPOLOGICAL SOLITONS IN U(1) × U(1) PLANAR GAUGE THEORY

1991 ◽  
Vol 06 (27) ◽  
pp. 2547-2553
Author(s):  
JUAN MATEOS GUILARTE
Keyword(s):  
Gauge Theory ◽  
Quantum Hall ◽  
Effective Field ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Topological Solitons ◽  
Mathematical Properties ◽  
Similar Solutions ◽  
Higgs Fields

A new of kind of stable topological solitons in a model of the type arising in the effective field theory for the fractional quantum Hall effect has been discovered. Similar solutions also exists in the standard U (1) × U (1) gauge theory of two complex Higgs fields with a quite general Higgs potential describing superconducting strings. The physical and mathematical properties of both types of solitons are discussed.

scholarly journals CHARGE AND STATISTICS OF QUASIPARTICLES IN FRACTIONAL QUANTUM HALL EFFECT

2006 ◽  
Vol 20 (32) ◽  
pp. 5405-5416
Author(s):  
B. BASU ◽  
P. BANDYOPADHYAY ◽  
S. DHAR
Keyword(s):  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Statistical Parameter ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Dynamical Phase ◽  
Numerical Studies ◽  
Laughlin Wave Function

We have studied here the charge and statistics of quasiparticle excitations in FQH states on the basis of the Berry phase approach incorporating the fact that even number of flux quanta can be gauged away when the Berry phase is removed to the dynamical phase. It is observed that the charge q and statistical parameter θ of a quasiparticle at filling factor ν = n/(2pn+1) are given by q = (n/2pn+1)e and θ = n/(2pn+1), with the fact that the charge of the quasihole is opposite to that of the quasielectron. Using Laughlin wave function for quasiparticles, numerical studies have been done following the work of Kjønsberg and Myrheim1 for FQH states at ν = 1/3 and it is pointed out that as in case of quasiholes, the statistics parameter can be well defined for quasielectrons having the value θ = 1/3.

scholarly journals PROPERTIES OF QUANTUM HALL SKYRMIONS FROM ANOMALIES

1998 ◽  
Vol 13 (32) ◽  
pp. 2627-2635 ◽  
Author(s):  
S. BAEZ ◽  
A. P. BALACHANDRAN ◽  
A. TRAVESSET ◽  
A. STERN
Keyword(s):  
Quantum Hall ◽  
Effective Field ◽  
Fractional Quantum Hall Effect ◽  
Spin Fluctuations ◽  
Winding Number ◽  
Anomaly Cancellation ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons

In this letter, we introduce Fractional Quantum Hall Effect (FQHE) Skyrmions in the Chern–Simons effective field theory description, and we present a new derivation of the FQHE Skyrmions properties, namely charge and spin, which results from considerations at the edge of the Hall sample. At the boundary, we demand anomaly cancellation for the chiral edge currents, as well as, allow for the possibility of Skyrmion creation and annihilation. For the Skyrmion charge and spin, we get the values eνN Sky and νN Sky /2, respectively, where e is electron charge, ν is the filling fraction and N Sky is the Skyrmion winding number. We also add terms to the action so that the classical spin fluctuations in the bulk satisfy the standard equations of a ferromagnet and find that spin waves propagate with the classical drift velocity of the electron.

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