Related papers: The quantum Hall hierarchy in spherical geometry
In the study of the quantum Hall effect there are still many unresolved problems. One of these is how to generate representative wave functions for ground states on other geometries than the planar and spherical. We study one such geometry,…
We construct a new representation of composite fermion wave functions in the lowest Landau level which enables Monte Carlo computations at arbitrary filling factors for a fairly large number of composite fermions, thus clearing the way…
Certain fractional quantum Hall wavefunctions -- particularly including the Laughlin, Moore-Read, and Read-Rezayi wavefunctions -- have special structure that makes them amenable to analysis using an exeptionally wide range of techniques…
The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is…
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…
In the conformal field theory (CFT) approach to the quantum Hall effect, the multi-electron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the…
The integer quantum Hall effect (IQHE) is usually modeled using Galilean-invariant or rotationally-invariant Landau levels. However, these are not generic symmetries of electrons moving in a crystalline background, even in the low-density…
Fractional quantum Hall liquids can accomodate various degrees of spatial ordering. The most likely scenarios are a Hall hexatic, Hall smectic, and Hall crystal, in which respectively orientational, one--dimensional translational, and…
We characterize in detail a wave function conceivable in fractional quantum Hall systems where a spin or equivalent degree of freedom is present. This wave function combines the properties of two previously proposed quantum Hall wave…
We consider quantum spin Hall effect in an anisotropic strip of stripes and address both integer and fractional filling factors. The first model is based on a gradient of spin-orbit interaction in the direction perpendicular to the stripes.…
Collective modes of exotic quantum fluids reveal underlying physical mechanisms responsible for emergent complex quantum ground states. We observe unexpected new collective modes in the fractional quantum Hall (FQH) regime:…
New trial wave functions corresponding to half filling quantum Hall states are proposed. These wave functions are constructed by first pairing up the quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative angular…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
In this article, we deal with the structure of the spherical Hall algebra of coherent sheaves with parabolic structures on a smooth projective curve of arbitrary genus. We provide a shuffle-like presentation of the vector bundle part and…
Orbital angular momentum eigenfunctions are readily understood in terms of spherical harmonic wavefunctions. However, the quantum mechanical phenomenon of spin is often said to be mysterious and hard to visualize, with no classical…
Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. Recent achievements in this direction, together with the possibility of tuning inter-particle interactions, suggest that…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
In the search of fractional quantum anomalous Hall (FQAH) effect, the conventional wisdom is to start from a flat Chern band isolated from the rest of the Hilbert space by band gaps, so that many-body interaction can be projected to a…
We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall (FQH) Hamiltonian. To find the set of degenerate ground states, we employ the infinite density…
We present here a complete microscopic theory of a family of neutral excitations in the fractional quantum Hall fluids, related to the geometric fluctuations of the quantum Hall ground states. Many of the physical properties of such…