14,515 research outputs found
The Fractional Quantum Hall States at and and their Non-Abelian Nature
We investigate the nature of the fractional quantum Hall (FQH) state at
filling factor , and its particle-hole conjugate state at ,
with the Coulomb interaction, and address the issue of possible competing
states. Based on a large-scale density-matrix renormalization group (DMRG)
calculation in spherical geometry, we present evidence that the physics of the
Coulomb ground state (GS) at and is captured by the
parafermion Read-Rezayi RR state, . We first establish that the
state at is an incompressible FQH state, with a GS protected by a
finite excitation gap, with the shift in accordance with the RR state. Then, by
performing a finite-size scaling analysis of the GS energies for
with different shifts, we find that the state has the lowest
energy among different competing states in the thermodynamic limit. We find the
fingerprint of topological order in the FQH and
states, based on their entanglement spectrum and topological entanglement
entropy, both of which strongly support their identification with the
state. Furthermore, by considering the shift-free
infinite-cylinder geometry, we expose two topologically-distinct GS sectors,
one identity sector and a second one matching the non-Abelian sector of the
Fibonacci anyonic quasiparticle, which serves as additional evidence for the
state at and .Comment: 12 pages, 8 figure
Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
The non-Abelian topological order has attracted a lot of attention for its
fundamental importance and exciting prospect of topological quantum
computation. However, explicit demonstration or identification of the
non-Abelian states and the associated statistics in a microscopic model is very
challenging. Here, based on density-matrix renormalization group calculation,
we provide a complete characterization of the universal properties of bosonic
Moore-Read state on Haldane honeycomb lattice model at filling number
for larger systems, including both the edge spectrum and the bulk anyonic
quasiparticle (QP) statistics. We first demonstrate that there are three
degenerating ground states, for each of which there is a definite anyonic flux
threading through the cylinder. We identify the nontrivial countings for the
entanglement spectrum in accordance with the corresponding conformal field
theory. Through inserting the charge flux, it is found that two of the
ground states can be adiabatically connected through a fermionic
charge- QP being pumped from one edge to the other, while the
ground state in Ising anyon sector evolves back to itself. Furthermore, we
calculate the modular matrices and , which contain
all the information for the anyonic QPs. In particular, the extracted quantum
dimensions, fusion rule and topological spins from modular matrices positively
identify the emergence of non-Abelian statistics following the
Chern-Simons theory.Comment: 5 pages; 3 figure
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