Related papers: Higher Dimensional Quantum Hall Effect as A-Class …
We develop a supersymmetric extension of Chern-Simons theory and Chern-Simons-Landau-Ginzburg theory for supersymmetric quantum Hall liquid. Supersymmetric counterparts of topological and gauge structures peculiar to the Chern-Simons theory…
Chiral topological insulator (AIII-class) with Landau levels is constructed based on the Nambu 3-algebraic geometry. We clarify the geometric origin of the chiral symmetry of the AIII-class topological insulator in the context of…
The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators - topologically non-trivial states of two-dimensional matter with broken…
In this work, we predict a hinged quantum spin-Hall (HQSH) effect featured by a pair of helical hinge modes in antiferromagnetic (AFM) topological insulator (TI) multilayers. This pair of helical hinge modes are localized on the hinges of…
The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee[1], analytical formula satisfied by the energy…
We derive a noncommutative U(1) and U(n) gauge theory on the fuzzy sphere from a three dimensional matrix model by expanding the model around a classical solution of the fuzzy sphere. Chern-Simons term is added in the matrix model to make…
Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a…
Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF gauge theory, respectively. We analyze…
In this paper, we study the non-commutative Chern-Simons description of the hierarchy of quantum Hall states. Our method is based on the framework suggested by Susskind in hep-th/0101029. By using the area preserving diffeomorphism gauge…
Magnetic topological states refer to a class of exotic phases in magnetic materials with their non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state,…
Topological phases of matter can be classified by using Clifford algebras through Bott periodicity. We consider effective topological field theories of quantum Hall systems and topological insulators that are Chern-Simons and BF field…
We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a…
We investigate the spectrum of the gauge theory with Chern-Simons term on the noncommutative plane, a modification of the description of the Quantum Hall fluid recently proposed by Susskind. We find a series of the noncommutative massive…
We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our…
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion…
We show the explicit connection between two distinct and complementary approaches to the fractional quantum Hall system (FQHS): the quantum wires formalism and the topological low-energy effective description given in terms of an Abelian…
We analyze some features of the entanglement entropy for an integer quantum Hall state ($\nu =1 $) in comparison with ideas from relativistic field theory and noncommutative geometry. The spectrum of the modular operator, for a restricted…
We derive a topological action that describes the confining phase of (Super-)Yang-Mills theories with gauge group $SU(N)$, similar to the work recently carried out by Seiberg and collaborators. It encodes all the Aharonov-Bohm phases of the…
The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like "spin" texture in momentum space.…