Related papers: $SO(5)$ Landau Models and Nested Nambu Matrix Geom…
This is an overview of recent progress in constructing and studying superextensions of the Landau problem of a quantum particle on a plane in the uniform magnetic field, as well as of its Haldane's $S^2$ generalization ({\tt hep-th/0311159,…
We discuss properties of an exactly SO(5) symmetric ladder model. In the strong coupling limit we demonstrate how the SO(3)-symmetric description of spin ladders in terms of bond Bosons can be upgraded to an SO(5)-symmetric bond-Boson…
When electrons moving in two-dimensions (2D) are subjected to a strong uniform magnetic field, they form flat bands called Landau levels, which are the basis for the quantum Hall effect. Landau levels can also arise from pseudomagnetic…
We consider, in a superspace, new operator dependent noncommutative (NC) geometries of the nonlinear quantum Hall limit related to classes of f-deformed Landau operators in the spherical harmonic well. Different NC coordinate algebras are…
We report on an exact diagonalization study of fractional quantum Hall states at filling factor $\nu=2/3$ in a system with a four-fold degenerate $n$=0 Landau level and SU(4) symmetric Coulomb interactions. Our investigation reveals…
We consider the quantum mechanics of a particle on the coset superspace $SU(2|1)/[U(1)\times U(1)]$, which is a super-flag manifold with $SU(2)/U(1)\cong S^2$ `body'. By incorporating the Wess-Zumino terms associated with the $U(1)\times…
In a recent article, we were motivated by the question of whether any of the remarkable condensed matter phenomena, such as the quantum Hall effect (QHE), the Integer quantum Hall effect (IQHE) etc., could potentially be observed in the…
In this paper, we revisit some quantum mechanical aspects related to the Quantum Hall Effect. We consider a Landau type model, paying a special attention to the experimental and geometrical features of Quantum Hall experiments. The…
The discovery of quantum Hall effect in two-dimensional (2D) electronic systems inspired the topological classifications of electronic systems1,2. By stacking 2D quantum Hall effects with interlayer coupling much weaker than the Landau…
We study numerically the so-called fundamental modular region Lambda, a region free of Gribov copies, in the minimal Landau gauge for pure SU(2) lattice gauge theory. To this end we evaluate the influence of Gribov copies on several…
We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a…
We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry…
We construct higher dimensional quantum Hall systems based on fuzzy spheres. It is shown that fuzzy spheres are realized as spheres in colored monopole backgrounds. The space noncommutativity is related to higher spins which is originated…
I give a brief review of higher dimensional quantum Hall effect (QHE) and how one can use a general framework to describe the lowest Landau level dynamics as a noncommutative field theory whose semiclassical limit leads to anomaly free…
We propose a geometric mechanism for fractional quantum Hall states based on impurity-induced correlations within a Landau level. A correlated distribution of ionized impurities partially modifies the Landau-level degeneracy through…
We use a mathematical framework that we introduced in a previous paper to study geometrical and quantum mechanical aspects of a Hall system with finite size and general boundary conditions. Geometrical structures control possibly the…
The critical properties of the real phi^4 scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a matrix (non commutative) discretisation of the algebra of functions on the usual two dimensional sphere. It is…
We propose a matrix model realisation of a three-dimensional quantum space. It has an onion-like structure composed of concentric fuzzy spheres of increasing radius. The angular part of the Laplace operator is inherited from that of the…
We give a brief review of the Quantum Hall effect in higher dimensions and its relation to fuzzy spaces. For a quantum Hall system, the lowest Landau level dynamics is given by a one-dimensional matrix action. This can be used to write down…
We prove three structural impossibility results demonstrating that fuzzy metric spaces cannot capture essential features of quantum state geometry. First, we show they cannot model destructive interference between concepts due to phase…