scholarly journals From Chern–Simons to Tomonaga–Luttinger

2018 ◽  
Vol 33 (02) ◽  
pp. 1850013 ◽  
Author(s):  
Nicola Maggiore
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Weyl Fermion

A single-sided boundary is introduced in the three-dimensional Chern–Simons model. It is shown that only one boundary condition for the gauge fields is possible, which plays the twofold role of chirality condition and bosonization rule for the two-dimensional Weyl fermion describing the degrees of freedom of the edge states of the Fractional Quantum Hall Effect. The symmetry on the boundary is derived, which determines the effective two-dimensional action, whose equation of motion coincides with the continuity equation of the Tomonaga–Luttinger theory. The role of Lorentz symmetry and of discrete symmetries on the boundary is also discussed.

Fractionally charged BPS particles in M-string on 3D orbifolds

2021 ◽  
Author(s):  
S. Boukaddid ◽  
R. Ahl Laamara ◽  
L. B. Drissi ◽  
E. H. Saidi ◽  
J. Zerouaoui
Keyword(s):  
Quantum Hall ◽  
Three Dimensional ◽  
Particle Spectrum ◽  
Gauge Bosons ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Super Conformal Field Theory ◽  
Bps States ◽  
Chern Simons

In this paper, we study the M-string realization of chiral [Formula: see text]-super-conformal field theory in 6 dimensions and its orbifold compactification down to three-dimensional (3D). We analyze its fractionally charged BPS particle spectrum in connection with effective 3D Chern–Simons gauge theory and the supersymmetric fractional quantum Hall effect in [Formula: see text] dimensions. We construct the set of underlying fractionally charged BPS particles in the ground state of the compactified M string and find that it contains 144 BPS states that are generated by four basic quasi-particles (two bosonic-like and two fermionic like) and their CPT conjugate. Two representations of the gauge bosons and the gauginos as condensates of the basic quasiparticles are found and explicit realizations are also given. Other features concerning generalizations are also discussed.

scholarly journals ON THE INTERACTION ENERGY OF TWO-DIMENSIONAL ELECTRON FQHE SYSTEMS WITHIN THE CHERN–SIMONS APPROACH

1999 ◽  
Vol 13 (17) ◽  
pp. 2263-2274
Author(s):  
PIOTR SITKO
Keyword(s):  
Interaction Energy ◽  
Quantum Hall ◽  
Electron System ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Cyclotron Energy ◽  
Dimensional Electron System ◽  
Chern Simons

The interaction energy of the two-dimensional electron system in the region of fractional quantum Hall effect is considered within the Chern–Simons composite fermion approach. In the limit when Coulomb interaction is very small comparing to the cyclotron energy the RPA results are obtained for the fillings ν=1/3, 1/5, 2/3, 2/5, 3/7 and compared with the exact diagonalization results for small systems (extrapolated for infinite systems). They show very poor agreement suggesting the need for looking for alternative approaches.

scholarly journals NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

QUANTUM COMPUTING WITH NON-ABELIAN QUASIPARTICLES

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1372-1378 ◽  
Author(s):  
N. E. BONESTEEL ◽  
L. HORMOZI ◽  
G. ZIKOS ◽  
S. H. SIMON
Keyword(s):  
Dimensional Space ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Operations ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
Two Space Dimensions ◽  
Topological Quantum Computation

In topological quantum computation quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum operations are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum operations depend only on the topology of the braids formed by these world-lines. We describe recent work showing how to find braids which can be used to perform arbitrary quantum computations using a specific kind of quasiparticle (those described by the so-called Fibonacci anyon model) which are thought to exist in the experimentally observed ν = 12/5 fractional quantum Hall state.

scholarly journals Graphene: A Peculiar Allotrope Of Carbon

2013 ◽  
Vol 3 ◽  
pp. 87-88
Author(s):  
Laxmi Nath Bhattarai
Keyword(s):  
Quantum Hall ◽  
Two Dimensional ◽  
Practical Application ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Effects ◽  
Hall Effects ◽  
Fractional Quantum Hall Effects ◽  
Relativistic Particles

Graphene is a two dimensional one atom thick allotrope of Carbon. Electrons in grapheme behave as massless relativistic particles. It is a 2 dimensional nanomaterial with many peculiar properties. In grapheme both integral and fractional quantum Hall effects are observed. Many practical application are seen from use of Graphene material.The Himalayan PhysicsVol. 3, No. 3, July 2012Page: 87-88

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