We investigate the non-universal part of the orbital entanglement spectrum (OES) of the nu = 1/3 fractional quantum Hall effect (FQH) ground-state with Coulomb interactions. The non-universal part of the spectrum is the part that is missing in the La
ughlin model state OES whose level counting is completely determined by its topological order. We find that the OES levels of the Coulomb interaction ground-state are organized in a hierarchical structure that mimic the excitation-energy structure of the model pseudopotential Hamiltonian which has a Laughlin ground state. These structures can be accurately modeled using Jains composite fermion quasihole-quasiparticle excitation wavefunctions. To emphasize the connection between the entanglement spectrum and the energy spectrum, we also consider the thermodynamical OES of the model pseudopotential Hamiltonian at finite temperature. The observed good match between the thermodynamical OES and the Coulomb OES suggests a relation between the entanglement gap and the true energy gap.
We extend the concept of entanglement spectrum from the geometrical to the particle bipartite partition. We apply this to several Fractional Quantum Hall (FQH) wavefunctions on both sphere and torus geometries to show that this new type of entangleme
nt spectra completely reveals the physics of bulk quasihole excitations. While this is easily understood when a local Hamiltonian for the model state exists, we show that the quasiholes wavefunctions are encoded within the model state even when such a Hamiltonian is not known. As a nontrivial example, we look at Jains composite fermion states and obtain their quasiholes directly from the model state wavefunction. We reach similar conclusions for wavefunctions described by Jack polynomials.
We investigate disordered graphene with strong long-range impurities. Contrary to the common belief that delocalization should persist in such a system against any disorder, as the system is ex-pected to be equivalent to a disordered two-dimensional
Dirac Fermionic system, we find that states near the Dirac points are localized for sufficiently strong disorder and the transition between the localized and delocalized states is of Kosterlitz-Thouless type. Our results show that the transition originates from bounding and unbounding of local current vortices.
We investigate the effect of topological defects on the transport properties of a narrow ballistic ribbon of graphene with zigzag edges. Our results show that the longitudinal conductance vanishes at several discrete Fermi energies where the system d
evelops loop orbital electric currents with certain chirality. The chirality depends on the direction of the applied bias voltage and the sign of the local curvature created by the topological defects. This novel quantum blockade phenomenon provides a new way to generate a magnetic moment by an external electric field, which can prove useful in carbon electronics.
