964 research outputs found
Search for exact local Hamiltonians for general fractional quantum Hall states
We report on our systematic attempts at finding local interactions for which
the lowest-Landau-level projected composite-fermion wave functions are the
unique zero energy ground states. For this purpose, we study in detail the
simplest non-trivial system beyond the Laughlin states, namely bosons at
filling and identify local constraints among clusters of
particles in the ground state. By explicit calculation, we show that no
Hamiltonian up to (and including) four particle interactions produces this
state as the exact ground state, and speculate that this remains true even when
interaction terms involving greater number of particles are included.
Surprisingly, we can identify an interaction, which imposes an energetic
penalty for a specific entangled configuration of four particles with relative
angular momentum of , that produces a unique zero energy solution (as
we have confirmed for up to 12 particles). This state, referred to as the
-state, is not identical to the projected composite-fermion state, but
the following facts suggest that the two might be topologically equivalent: the
two sates have a high overlap; they have the same root partition; the quantum
numbers for their neutral excitations are identical; and the quantum numbers
for the quasiparticle excitations also match. On the quasihole side, we find
that even though the quantum numbers of the lowest energy states agree with the
prediction from the composite-fermion theory, these states are not separated
from the others by a clearly identifiable gap. This prevents us from making a
conclusive claim regarding the topological equivalence of the state
and the composite-fermion state. Our study illustrates how new candidate states
can be identified from constraining selected many particle configurations and
it would be interesting to pursue their topological classification.Comment: 21 pages, 11 figure
Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
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 Laughlin 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
Jain's "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.Comment: 16 pages, 19 figure
The KOH terms and classes of unimodal N-modular diagrams
We show how certain suitably modified N-modular diagrams of integer
partitions provide a nice combinatorial interpretation for the general term of
Zeilberger's KOH identity. This identity is the reformulation of O'Hara's
famous proof of the unimodality of the Gaussian polynomial as a combinatorial
identity. In particular, we determine, using different bijections, two main
natural classes of modular diagrams of partitions with bounded parts and
length, having the KOH terms as their generating functions. One of our results
greatly extends recent theorems of J. Quinn et al., which presented striking
applications to quantum physics.Comment: Several mostly minor or notational changes with respect to the first
version, in response to the referees' comments. 13 pages, 3 figures. To
appear in JCT
Unified Fock space representation of fractional quantum Hall states
Many bosonic (fermionic) fractional quantum Hall states, such as Laughlin,
Moore-Read and Read-Rezayi wavefunctions, belong to a special class of
orthogonal polynomials: the Jack polynomials (times a Vandermonde determinant).
This fundamental observation allows to point out two different recurrence
relations for the coefficients of the permanent (Slater) decomposition of the
bosonic (fermionic) states. Here we provide an explicit Fock space
representation for these wavefunctions by introducing a two-body squeezing
operator which represents them as a Jastrow operator applied to reference
states, which are in general simple periodic one dimensional patterns.
Remarkably, this operator representation is the same for bosons and fermions,
and the different nature of the two recurrence relations is an outcome of
particle statistics.Comment: 10 pages, 3 figure
The structure of spinful quantum Hall states: a squeezing perspective
We provide a set of rules to define several spinful quantum Hall model
states. The method extends the one known for spin polarized states. It is
achieved by specifying an undressed root partition, a squeezing procedure and
rules to dress the configurations with spin. It applies to both the
excitation-less state and the quasihole states. In particular, we show that the
naive generalization where one preserves the spin information during the
squeezing sequence, may fail. We give numerous examples such as the Halperin
states, the non-abelian spin-singlet states or the spin-charge separated
states. The squeezing procedure for the series (k=2,r) of spinless quantum Hall
states, which vanish as r powers when k+1 particles coincide, is generalized to
the spinful case. As an application of our method, we show that the counting
observed in the particle entanglement spectrum of several spinful states
matches the one obtained through the root partitions and our rules. This
counting also matches the counting of quasihole states of the corresponding
model Hamiltonians, when the latter is available.Comment: 19 pages, 7 figures; v2: minor changes, and added references.
Mathematica packages are available for downloa
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