Zi-Xiang Hu

Fractional quantum Hall effect at ν = 5 ∕ 2 : Ground states, non-Abelian quasiholes, and edge modes in a microscopic model

We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction

Construction of edge states in fractional quantum Hall systems by Jack polynomials

\ensuremath{\nu}=5∕2

Quantum Hall effects in fast-rotating Fermi gases with anisotropic dipolar interaction

, based on the disk geometry. Our model includes Coulomb interaction and a semirealistic confining potential. We also mix in a three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read-like state. From the evolution of the edge spectrum, we obtain the velocities of the charge and neutral edge modes, which turn out to be very different. This separation of velocities is a source of decoherence for a non-Abelian quasihole and/or quasiparticle (with charge

Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect

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Realizing universal edge properties in graphene fractional quantum Hall liquids.

) when propagating at the edge; using numbers obtained from a specific set of parameters, we estimate the decoherence length to be around

Edge-mode velocities and thermal coherence of quantum Hall interferometers

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Quasiparticle tunneling in the Moore-Read fractional quantum Hall State

. This sets an upper bound for the separation of the two point contacts in a double point-contact interferometer, designed to detect the non-Abelian nature of such quasiparticles. We also find a state that is a potential candidate for the recently proposed anti-Pfaffian state. We find the speculated anti-Pfaffian state is favored in weak confinement (smooth edge), while the Moore-Read Pfaffian state is favored in strong confinement (sharp edge).

Anisotropic pseudopotential characterization of quantum Hall systems under a tilted magnetic field

We study the edge-mode excitations of a fractional quantum Hall droplet by expressing the edge state wavefunctions as linear combinations of Jack polynomials with a negative parameter. We show that the exact diagonalization within subspace of Jack polynomials can be used to generate the chiral edge-mode excitation spectrum in the Laughlin phase and the Moore-Read phase with realistic Coulomb interaction. The truncation technique for the edge excitations simplifies the procedure to extract reliably the edge-mode velocities, which avoids the otherwise complicated analysis of the full spectrum that contains both edge and bulk excitations. Generalization to the Read-Rezayi state is also discussed.

Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries

We investigate fast rotating quasi-two-dimensional dipolar Fermi gases in the quantum Hall regime. By tuning the direction of the dipole moments with respect to the z axis, the dipole-dipole interaction becomes anisotropic in the x-y plane. For a soft confining potential we find that, as we tilt the angle of the dipole moments, the system evolves from v = 1/3 Laughlin state with dipoles being polarized along the z axis to a series of ground states characterized by distinct mean total angular momentum, and finally to an anisotropic integer quantum Hall state. During the transition from the fractional regime to the integer regime, we find that the density profile of the system exhibits crystal-like structures. We map out the ground states as a function of the tilt angle and the confining potential, revealing the competition of the isotropic confining potential and both the isotropic and anisotropic components of the dipole-dipole interaction.

Edge states at the interface between monolayer and bilayer graphene

We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems that are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. This formalism allows us to expand any translation-invariant interaction over a complete basis, and directly reveals the intrinsic metric of incompressible FQH fluids. We show that purely anisotropic pseudopotentials give rise to new types of bound states for small particle clusters in the infinite plane, and can be used as a diagnostic of FQH nematic order. We also demonstrate that generalized pseudopotentials quantify the anisotropic contribution to the effective interaction potential, which can be particularly large in models of fractional Chern insulators.