Related papers: A Matrix Model for Non-Abelian Quantum Hall States
The Moore-Read state is one the most well known non-Abelian fractional quantum Hall states. It supports non-Abelian Ising anyons in the bulk and a chiral bosonic and chiral Majorana modes on the boundary. It has been recently conjectured…
We propose a novel geometric model of three-dimensional topological insulators in presence of an external electromagnetic field. The gapped boundary of these systems supports relativistic quantum Hall states and is described by a…
We present a pure Chern-Simons formulation of families of interesting Conformal Field Theories describing edge states of non-Abelian Quantum Hall states. These theories contain two Abelian Chern-Simons fields describing the…
We provide a detailed explanation of the formalism necessary to construct matrix product states for non-Abelian quasiholes in fractional quantum Hall model states. Our construction yields an efficient representation of the wave functions…
We provide evidence for conjectural dualities between nonrelativistic Chern-Simons-matter theories and theories of (fractional, nonAbelian) quantum Hall fluids in $2+1$ dimensions. At low temperatures, the dynamics of nonrelativistic…
We consider quantum Hall states on a space with boundary, focusing on the aspects of the edge physics which are completely determined by the symmetries of the problem. There are four distinct terms of Chern-Simons type that appear in the…
We propose a quantum matrix oscillator as a model that provides the construction of the quantum Hall states in a direct way. A connection of this model to the regularized matrix model introduced by Polychronakos is established . By…
We construct 1D and 2D long-range SU(N) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N) level 1 WZW model. Since the resulting…
Model quantum Hall states including Laughlin, Moore-Read and Read-Rezayi states are generalized into appropriate anisotropic form. The generalized states are exact zero-energy eigenstates of corresponding anisotropic two- or multi-body…
Motivated by a recent experiment reporting the fractional quantum spin Hall effect in twisted ${\rm MoTe}_2$, we investigate microscopically the prospects of realizing exotic topologically ordered states beyond conventional quantum Hall…
We propose two non-abelian Chern-Simons matrix models as the effective descriptions of 4-dimensional quantum Hall fluids. One of them describes a new type of 4-dimensional quantum Hall fluid on the space of quaternions, the other provides…
We formulate a field theory for a class of spin-singlet quantum Hall states (the Haldane-Rezayi state and its variants) which have been proposed for the quantized Hall plateaus observed at the second lowest Landau level. A new essential…
We propose a frustration-free model for the Moore-Read quantum Hall state on sufficiently thin cylinders with circumferences $\lesssim 7$ magnetic lengths. While the Moore-Read Hamiltonian involves complicated long-range interactions…
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…
We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus…
We study some aspects of recent proposals to use the noncommutative Chern-Simons theory as an effective description of some planar condensed matter models in strong magnetic fields, such as the Quantum Hall Effect. We present an alternative…
By allowing the spin degrees of freedom, we present a generalized spin allowed $U(1)\times U(1)$ Chern-Simons theory of fractional quantum Hall effects for odd and even denominator filling factors in single layers. This theory is shown to…
A class of exact spin ground states with nonzero averages of vector spin chirality, $<\v{S}_i \times \v{S}_j \cdot \hat{z}>$, is presented. It is obtained by applying non-uniform O(2) rotations of spin operators in the XY plane on the…
We propose a family of Abelian quantum Hall states termed the non-diagonal states, which arise at filling factors $\nu=p/2q$ for bosonic systems and $\nu=p/(p+2q)$ for fermionic systems, with $p$ and $q$ being two coprime integers.…
We have studied the partially spin-polarized fractional quantum Hall states using Chern Simon's theory and plasma picture proposed by Halperin. Using these theoretical techniques we have tried to find the stable polarized states of…