1,003 research outputs found
Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
Using the newly developed Matrix Product State (MPS) formalism for
non-abelian Fractional Quantum Hall (FQH) states, we address the question of
whether a FQH trial wave function written as a correlation function in a
non-unitary Conformal Field Theory (CFT) can describe the bulk of a gapped FQH
phase. We show that the non-unitary Gaffnian state exhibits clear signatures of
a pathological behavior. As a benchmark we compute the correlation length of
Moore-Read state and find it to be finite in the thermodynamic limit. By
contrast, the Gaffnian state has infinite correlation length in (at least) the
non-Abelian sector, and is therefore gapless. We also compute the topological
entanglement entropy of several non-abelian states with and without quasiholes.
For the first time in FQH the results are in excellent agreement in all
topological sectors with the CFT prediction for unitary states. For the
non-unitary Gaffnian state in finite size systems, the topological entanglement
entropy seems to behave like that of the Composite Fermion Jain state at equal
filling.Comment: 5 pages, 5 figures, and supplementary material. Published versio
Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
We derive an exact matrix product state representation of the Haldane-Rezayi
state on both the cylinder and torus geometry. Our derivation is based on the
description of the Haldane-Rezayi state as a correlator in a non-unitary
logarithmic conformal field theory. This construction faithfully captures the
ten degenerate ground states of this model state on the torus. Using the
cylinder geometry, we probe the gapless nature of the phase by extracting the
correlation length, which diverges in the thermodynamic limit. The numerically
extracted topological entanglement entropies seem to only probe the Abelian
part of the theory, which is reminiscent of the Gaffnian state, another model
state deriving from a non-unitary conformal field theory.Comment: Corrected labels in Fig.
Braiding non-Abelian quasiholes in fractional quantum Hall states
Quasiholes in certain fractional quantum Hall states are promising candidates
for the experimental realization of non-Abelian anyons. They are assumed to be
localized excitations, and to display non-Abelian statistics when sufficiently
separated, but these properties have not been explicitly demonstrated except
for the Moore-Read state. In this work, we apply the newly developed matrix
product state technique to examine these exotic excitations. For the Moore-Read
and the Read-Rezayi states, we estimate the quasihole radii, and
determine the correlation lengths associated with the exponential convergence
of the braiding statistics. We provide the first microscopic verification for
the Fibonacci nature of the Read-Rezayi quasiholes. We also
present evidence for the failure of plasma screening in the non-unitary
Gaffnian wave function.Comment: 9 pages, 9 figures; published versio
Matrix product state representation of non-Abelian quasiholes
We provide a detailed explanation of the formalism necessary to construct
matrix product states for non-Abelian quasiholes in fractional quantum Hall
model states. Our construction yields an efficient representation of the wave
functions with conformal-block normalization and monodromy, and complements the
matrix product state representation of fractional quantum Hall ground states.Comment: 14 pages, 2 figures; published versio
Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry
We show that a large class of bosonic spin-singlet Fractional Quantum Hall
model wave-functions and their quasi-hole excitations can be written in terms
of Jack polynomials with a prescribed symmetry. Our approach describes new
spin-singlet quantum Hall states at filling fraction nu = 2k/(2r-1) and
generalizes the (k,r) spin-polarized Jack polynomial states. The NASS and
Halperin spin singlet states emerge as specific cases of our construction. The
polynomials express many-body states which contain configurations obtained from
a root partition through a generalized squeezing procedure involving spin and
orbital degrees of freedom. The corresponding generalized Pauli principle for
root partitions is obtained, allowing for counting of the quasihole states. We
also extract the central charge and quasihole scaling dimension, and propose a
conjecture for the underlying CFT of the (k, r) spin-singlet Jack states.Comment: 17 pages, 1 figur
Matrix Product State description of the Halperin States
Many fractional quantum Hall states can be expressed as a correlator of a
given conformal field theory used to describe their edge physics. As a
consequence, these states admit an economical representation as an exact Matrix
Product States (MPS) that was extensively studied for the systems without any
spin or any other internal degrees of freedom. In that case, the correlators
are built from a single electronic operator, which is primary with respect to
the underlying conformal field theory. We generalize this construction to the
archetype of Abelian multicomponent fractional quantum Hall wavefunctions, the
Halperin states. These latest can be written as conformal blocks involving
multiple electronic operators and we explicitly derive their exact MPS
representation. In particular, we deal with the caveat of the full wavefunction
symmetry and show that any additional SU(2) symmetry is preserved by the
natural MPS truncation scheme provided by the conformal dimension. We use our
method to characterize the topological order of the Halperin states by
extracting the topological entanglement entropy. We also evaluate their bulk
correlation length which are compared to plasma analogy arguments.Comment: 23 pages, 16 figure
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