A CONFORMAL FIELD THEORY DESCRIPTION OF THE PAIRED AND PARAFERMIONIC STATES IN THE QUANTUM HALL EFFECT

DOI10.1142/S021773230000219XzbMath0969.81070arXivcond-mat/0003453MaRDI QIDQ4523565

Vincenzo E. Marotta, Gerardo Cristofano, Giuseppe Maiella

Publication date: 14 January 2001

Published in: Modern Physics Letters A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0003453

zbMATH Keywords

scalar fieldsground state wave functionKac-Moody algebravertex operatorparafermionstwisted boundary conditionschiral primary fieldsquantum Hall fluidJain hierarchical fillingsnonstandard fillingsquasi-hole excitations

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Many-body theory; quantum Hall effect (81V70)

Related Items (14)

DISSIPATIVE QUANTUM MECHANICS AND KONDO-LIKE IMPURITIES ON NONCOMMUTATIVE TWO-TORI ⋮ TUNNELING EFFECTS IN A BRANE SYSTEM AND QUANTUM HALL PHYSICS ⋮ A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states ⋮ Paired quantum Hall states on noncommutative two-tori ⋮ Twisted CFT and bilayer quantum Hall systems in the presence of an impurity ⋮ Fully frustrated Josephson junction ladders with Möbius boundary conditions as topologically protected qubits ⋮ A twisted conformal field theory description of dissipative quantum mechanics ⋮ Topologically protected qubits as minimal Josephson junction arrays with non-trivial boundary conditions: a proposal ⋮ “Composite particles” and the eigenstates of Calogero–Sutherland and Ruijsenaars–Schneider ⋮ Paired states on a torus ⋮ Twisted conformal field theories and Morita equivalence ⋮ CFT description of the fully frustratedXYmodel and phase diagram analysis ⋮ A general CFT model for antiferromagnetic spin-1/2 ladders with Mobius boundary conditions ⋮ The \(\nu=5/2\) quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between Abelian and non-Abelian statistics

Cites Work

• A Chern-Simons effective field theory for the Pfaffian quantum Hall state
• \(\mathcal W_k\) structure of \(\widehat{\text{SU}}(2)\)-level \(k\) from covariant construction of Kac-Moody algebras
• Landau-Ginzburg theories for non-abelian quantum Hall states
• A unified conformal field theory description of paired quantum Hall states
• \(2n\)-quasihole states realize \(2^{n-1}\)-dimensional spinor braiding statistics in paired quantum Hall states
• THE QUANTUM HALL EFFECT AT ARBITRARY RATIONAL FILLING: A PROPOSAL
• CONFORMAL FIELD THEORY ON Z_k-SURFACES WITH EXCHANGE INTERACTIONS
• STRESS–TENSOR FOR PARAFERMIONS FROM WINDING SUBALGEBRAS OF AFFINE ALGEBRAS

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