相关论文: The Geometry of Quantum Hall Effect: An Effective …
Generalizing from previous work on the integer quantum Hall effect, we construct the effective action for the analog of Laughlin states for the fractional quantum Hall effect in higher dimensions. The formalism is a generalization of the…
An effective action for the bulk dynamics of quantum Hall effect in arbitrary even spatial dimensions was obtained some time ago in terms of a Chern-Simons term associated with the Dolbeault index theorem. Here we explore further properties…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
The effective action of (2+1)-dimensional QED with finite fermion density is calculated in a uniform electromagnetic field. It is shown that the integer quantum Hall effect and de Haas-van Alphen like phenomena in condensed matter physics…
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…
We give a brief review of 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 whose large $N$ limit produces an…
For a particle confined to the two-dimensional helical surface embedded in four-dimensional (4D) Euclidean space, the effective Hamiltonian is deduced in the thin-layer quantization formalism. We find that the gauge structure of the…
Quantum effects play an important role in quantum measurement theory. The set of all quantum effects can be organized into an algebraical structure called effect algebra. In this paper, we study various topologies on the Hilbert space…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some…
It is demonstrated that all observed fractions at moderate Landau level fillings in the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
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…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of…
Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to novel…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
We clarify relations between the higher dimensional quantum Hall effect and A-class topological insulator. In particular, we elucidate physical implications of the higher dimensional non-commutative geometry in the context of A-class…
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 analyze the Landau problem and quantum Hall effect on $S^3$ taking a constant background field proportional to the spin connection on $S^3$. The effective strength of the field can be tuned by changing the dimension of the representation…
The methods of quantum field theory are widely used in condensed matter physics. In particular, the concept of an effective action was proven useful when studying low temperature and long distance behavior of condensed matter systems. Often…