4 research outputs found
Topological Entanglement and Clustering of Jain Hierarchy States
We obtain the clustering properties and part of the structure of zeroes of
the Jain states at filling : they are a direct product of a
Vandermonde determinant (which has to exist for any fermionic state) and a
bosonic polynomial at filling which vanishes when
particles cluster together. We show that all Jain states satisfy a "squeezing
rule" (they are "squeezed polynomials") which severely reduces the dimension of
the Hilbert space necessary to generate them. The squeezing rule also proves
the clustering conditions that these states satisfy. We compute the topological
entanglement spectrum of the Jain state and compare it to both the
Coulomb ground-state and the non-unitary Gaffnian state. All three states have
very similar "low energy" structure. However, the Jain state entanglement
"edge" state counting matches both the Coulomb counting as well as two
decoupled U(1) free bosons, whereas the Gaffnian edge counting misses some of
the "edge" states of the Coulomb spectrum. The spectral decomposition as well
as the edge structure is evidence that the Jain state is universally equivalent
to the ground state of the Coulomb Hamiltonian at . The evidence is
much stronger than usual overlap studies which cannot meaningfully
differentiate between the Jain and Gaffnian states. We compute the entanglement
gap and present evidence that it remains constant in the thermodynamic limit.
We also analyze the dependence of the entanglement gap and overlap as we drive
the composite fermion system through a phase transition.Comment: 7 pages, 8 figure
The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
We deduce a new set of symmetries and relations between the coefficients of
the expansion of Abelian and Non-Abelian Fractional Quantum Hall (FQH) states
in free (bosonic or fermionic) many-body states. Our rules allow to build an
approximation of a FQH model state with an overlap increasing with growing
system size (that may sometimes reach unity!) while using a fraction of the
original Hilbert space. We prove these symmetries by deriving a previously
unknown recursion formula for all the coefficients of the Slater expansion of
the Laughlin, Read Rezayi and many other states (all Jacks multiplied by
Vandermonde determinants), which completely removes the current need for
diagonalization procedures.Comment: modify comment in Ref. 1
Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
We present a general method to obtain the central charge and quasihole
scaling dimension directly from groundstate and quasihole wavefunctions. Our
method applies to wavefunctions satisfying specific clustering properties. We
then use our method to examine the relation between Jack symmetric functions
and certain W-algebras. We add substantially to the evidence that the (k,r)
admissible Jack functions correspond to correlators of the conformal field
theory W_k(k+1,k+r), by calculating the central charge and scaling dimensions
of some of the fields in both cases and showing that they match. For the Jacks
described by unitary W-models, the central charge and quasihole exponents match
the ones previously obtained from analyzing the physics of the edge
excitations. For the Jacks described by non-unitary W-models the central charge
and quasihole scaling dimensions obtained from the wavefunctions differ from
the ones obtained from the edge physics, which instead agree with the
"effective" central charge of the corresponding W-model.Comment: 22 pages, no figure
Entanglement spectra of critical and near-critical systems in one dimension
The entanglement spectrum of a pure state of a bipartite system is the full
set of eigenvalues of the reduced density matrix obtained from tracing out one
part. Such spectra are known in several cases to contain important information
beyond that in the entanglement entropy. This paper studies the entanglement
spectrum for a variety of critical and near-critical quantum lattice models in
one dimension, chiefly by the iTEBD numerical method, which enables both
integrable and non-integrable models to be studied. We find that the
distribution of eigenvalues in the entanglement spectra agrees with an
approximate result derived by Calabrese and Lefevre to an accuracy of a few
percent for all models studied. This result applies whether the correlation
length is intrinsic or generated by the finite matrix size accessible in iTEBD.
For the transverse Ising model, the known exact results for the entanglement
spectrum are used to confirm the validity of the iTEBD approach. For more
general models, no exact result is available but the iTEBD results directly
test the hypothesis that all moments of the reduced density matrix are
determined by a single parameter.Comment: 6 pages, 5 figure