8 research outputs found
Extracting Excitations From Model State Entanglement
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 entanglement 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 Jain's composite fermion states and obtain their
quasiholes directly from the model state wavefunction. We reach similar
conclusions for wavefunctions described by Jack polynomials.Comment: 5 pages, 7 figures, updated versio
Real-Space Entanglement Spectrum of Quantum Hall States
We investigate the entanglement spectra arising from sharp real-space
partitions of the system for quantum Hall states. These partitions differ from
the previously utilized orbital and particle partitions and reveal
complementary aspects of the physics of these topologically ordered systems. We
show, by constructing one to one maps to the particle partition entanglement
spectra, that the counting of the real-space entanglement spectra levels for
different particle number sectors versus their angular momentum along the
spatial partition boundary is equal to the counting of states for the system
with a number of (unpinned) bulk quasiholes excitations corresponding to the
same particle and flux numbers. This proves that, for an ideal model state
described by a conformal field theory, the real-space entanglement spectra
level counting is bounded by the counting of the conformal field theory edge
modes. This bound is known to be saturated in the thermodynamic limit (and at
finite sizes for certain states). Numerically analyzing several ideal model
states, we find that the real-space entanglement spectra indeed display the
edge modes dispersion relations expected from their corresponding conformal
field theories. We also numerically find that the real-space entanglement
spectra of Coulomb interaction ground states exhibit a series of branches,
which we relate to the model state and (above an entanglement gap) to its
quasiparticle-quasihole excitations. We also numerically compute the
entanglement entropy for the nu=1 integer quantum Hall state with real-space
partitions and compare against the analytic prediction. We find that the
entanglement entropy indeed scales linearly with the boundary length for large
enough systems, but that the attainable system sizes are still too small to
provide a reliable extraction of the sub-leading topological entanglement
entropy term.Comment: 13 pages, 11 figures; v2: minor corrections and formatting change
Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
We report the observation of a new series of Abelian and non-Abelian
topological states in fractional Chern insulators (FCI). The states appear at
bosonic filling nu= k/(C+1) (k, C integers) in several lattice models, in
fractionally filled bands of Chern numbers C>=1 subject to on-site Hubbard
interactions. We show strong evidence that the k=1 series is Abelian while the
k>1 series is non-Abelian. The energy spectrum at both groundstate filling and
upon the addition of quasiholes shows a low-lying manifold of states whose
total degeneracy and counting matches, at the appropriate size, that of the
Fractional Quantum Hall (FQH) SU(C) (color) singlet k-clustered states
(including Halperin, non-Abelian spin singlet states and their
generalizations). The groundstate momenta are correctly predicted by the FQH to
FCI lattice folding. However, the counting of FCI states also matches that of a
spinless FQH series, preventing a clear identification just from the energy
spectrum. The entanglement spectrum lends support to the identification of our
states as SU(C) color-singlets but offers new anomalies in the counting for
C>1, possibly related to dislocations that call for the development of new
counting rules of these topological states.Comment: 12 pages with supplemental material, 20 figures, published versio
Interacting bosons in topological optical flux lattices
An interesting route to the realization of topological Chern bands in
ultracold atomic gases is through the use of optical flux lattices. These
models differ from the tight-binding real-space lattice models of Chern
insulators that are conventionally studied in solid-state contexts. Instead,
they involve the coherent coupling of internal atomic (spin) states, and can be
viewed as tight-binding models in reciprocal space. By changing the form of the
coupling and the number of internal spin states, they give rise to Chern
bands with controllable Chern number and with nearly flat energy dispersion. We
investigate in detail how interactions between bosons occupying these bands can
lead to the emergence of fractional quantum Hall states, such as the Laughlin
and Moore-Read states. In order to test the experimental realization of these
phases, we study their stability with respect to band dispersion and band
mixing. We also probe novel topological phases that emerge in these systems
when the Chern number is greater than 1.Comment: 14 pages, 19 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
Entanglement entropy of integer Quantum Hall states in polygonal domains
The entanglement entropy of the integer Quantum Hall states satisfies the
area law for smooth domains with a vanishing topological term. In this paper we
consider polygonal domains for which the area law acquires a constant term that
only depends on the angles of the vertices and we give a general expression for
it. We study also the dependence of the entanglement spectrum on the geometry
and give it a simple physical interpretation.Comment: 8 pages, 6 figure