scholarly journals Hamiltonian Formulation of Quantum Hall Skyrmions with Hopf Term

1997 ◽  
Vol 12 (09) ◽  
pp. 619-630 ◽  
Author(s):  
B. Chakraborty ◽  
T. R. Govindarajan
Keyword(s):  
Angular Momentum ◽  
Sigma Model ◽  
Quantum Hall ◽  
Hamiltonian Formulation ◽  
Nonlinear Sigma Model ◽  
Quantum Hall Systems ◽  
Hamiltonian Analysis

We study the nonrelativistic nonlinear sigma model with Hopf term in this letter. This is an important issue because of its relation to the currently interesting studies in skyrmions in quantum Hall systems. We perform the Hamiltonian analysis of this system in CP1 variables. When the coefficient of the Hopf term becomes zero we get the Landau–Lifshitz description of the ferromagnets. The addition of Hopf term dramatically alters the Hamiltonian analysis. The spin algebra is modified giving a new structure and interpretation to the system. We point out momentum and angular momentum generators and new features they bring into the system.

scholarly journals QUANTUM HALL SKYRMIONS IN THE FRAMEWORK OF O(4) NONLINEAR SIGMA MODEL

2004 ◽  
Vol 18 (02) ◽  
pp. 171-184
Author(s):  
B. BASU ◽  
S. DHAR ◽  
P. BANDYOPADHYAY
Keyword(s):  
Sigma Model ◽  
Quantum Hall ◽  
Nonlinear Sigma Model ◽  
New Framework ◽  
Spin And Statistics

A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a θ-term determines the spin and statistics of these skyrmions.

ADIABATIC ROTATION FOR THE SKYRMIONS

1993 ◽  
Vol 08 (37) ◽  
pp. 3569-3573
Author(s):  
ZHONG-SHUI MA
Keyword(s):  
Angular Momentum ◽  
Gauge Field ◽  
Sigma Model ◽  
Poynting Vector ◽  
Electromagnetic Properties ◽  
Nonlinear Sigma Model ◽  
Fractional Statistics ◽  
Rotation Procedure ◽  
Chern Simons ◽  
Explicit Derivation

We study the electromagnetic properties of the skyrmions of the O(3) nonlinear sigma model in (2+1) dimensions coupled with the Chern-Simons field by the adiabatic rotation procedure. It is shown that there is no Poynting vector for the skyrmion configuration and the Chern-Simons gauge field. In the process, an explicit derivation of the angular momentum is presented, which connects with the fractional statistics for the skyrmions.

QUASIPARTICLE INTERACTIONS IN FRACTIONAL QUANTUM HALL SYSTEMS

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3545-3548
Author(s):  
A. WOJS ◽  
K.-S. YI ◽  
J. J. QUINN
Keyword(s):  
Angular Momentum ◽  
Interaction Energy ◽  
Landau Level ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Small Systems ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Numerical Studies

A partially filled shell (Landau level) of Laughlin quasiparticles (QP's) gives rise to an incompressible daughter state if the QP's themselves are Laughlin correlated. This occurs only if the pseudopotential V QP (L′) describing the interaction energy of a QP pair as a function of the total pair angular momentum L′ satisfies special conditions. V QP (L′) can be obtained quite accurately from numerical studies of small systems. It does not always satisfy these conditions (e.g. for quasielectrons of the Laughlin ν=1/3 state at their ν QE =1/3 filling). In such cases, formation of pairs or larger clusters may explain the recently observed incompressible states (like ν=4/11).

scholarly journals Controllable quantum point junction on the surface of an antiferromagnetic topological insulator

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Nicodemos Varnava ◽  
Justin H. Wilson ◽  
J. H. Pixley ◽  
David Vanderbilt
Keyword(s):  
Topological Insulator ◽  
Information Science ◽  
Domain Walls ◽  
Quantum Hall ◽  
Edge State ◽  
Wave Functions ◽  
Quantum Hall Systems ◽  
Electron Quantum ◽  
Quantum Point ◽  
Higher Temperature

AbstractEngineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

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