46 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
Coupled Atomic Wires in a Synthetic Magnetic Field
We propose and study systems of coupled atomic wires in a perpendicular
synthetic magnetic field as a platform to realize exotic phases of quantum
matter. This includes (fractional) quantum Hall states in arrays of many wires
inspired by the pioneering work [Kane et al. PRL {\bf{88}}, 036401 (2002)], as
well as Meissner phases and Vortex phases in double-wires. With one continuous
and one discrete spatial dimension, the proposed setup naturally complements
recently realized discrete counterparts, i.e. the Harper-Hofstadter model and
the two leg flux ladder, respectively. We present both an in-depth theoretical
study and a detailed experimental proposal to make the unique properties of the
semi-continuous Harper-Hofstadter model accessible with cold atom experiments.
For the minimal setup of a double-wire, we explore how a sub-wavelength spacing
of the wires can be implemented. This construction increases the relevant
energy scales by at least an order of magnitude compared to ordinary optical
lattices, thus rendering subtle many-body phenomena such as Lifshitz
transitions in Fermi gases observable in an experimentally realistic parameter
regime. For arrays of many wires, we discuss the emergence of Chern bands with
readily tunable flatness of the dispersion and show how fractional quantum Hall
states can be stabilized in such systems. Using for the creation of optical
potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail
how the coupled atomic wire setups can be realized in non-planar geometries
such as cylinders, discs, and tori
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
Particle Entanglement Spectra for Quantum Hall states on Lattices
We use particle entanglement spectra to characterize bosonic quantum Hall
states on lattices, motivated by recent studies of bosonic atoms on optical
lattices. Unlike for the related problem of fractional Chern insulators, very
good trial wavefunctions are known for fractional quantum Hall states on
lattices. We focus on the entanglement spectra for the Laughlin state at
for the non-Abelian Moore-Read state at . We undertake a
comparative study of these trial states to the corresponding groundstates of
repulsive two-body or three-body contact interactions on the lattice. The
magnitude of the entanglement gap is studied as a function of the interaction
strength on the lattice, giving insights into the nature of Landau-level
mixing. In addition, we compare the performance of the entanglement gap and
overlaps with trial wavefunctions as possible indicators for the topological
order in the system. We discuss how the entanglement spectra allow to detect
competing phases such as a Bose-Einstein condensate.Comment: 12 pages, 9 figure
Creating a bosonic fractional quantum Hall state by pairing fermions
We numerically study the behavior of spin-- fermions on a
two-dimensional square lattice subject to a uniform magnetic field, where
opposite spins interact via an on-site attractive interaction. Starting from
the non-interacting case where each spin population is prepared in a quantum
Hall state with unity filling, we follow the evolution of the system as the
interaction strength is increased. Above a critical value and for sufficiently
low flux density, we observe the emergence of a twofold quasidegeneracy
accompanied by the opening of an energy gap to the third level. Analysis of the
entanglement spectra shows that the gapped ground state is the bosonic
Laughlin state. Our work therefore provides compelling evidence of a
topological phase transition from the fermionic quantum Hall state at unity
filling to the bosonic Laughlin state at a critical attraction strength
Bosonic integer quantum Hall effect in optical flux lattices.
In two dimensions strongly interacting bosons in a magnetic field can realize a bosonic integer quantum Hall state, the simplest two-dimensional example of a symmetry-protected topological phase. We propose a realistic implementation of this phase using an optical flux lattice. Through exact diagonalization calculations, we show that the system exhibits a clear bulk gap and the topological signature of the bosonic integer quantum Hall state. In particular, the calculation of the many-body Chern number leads to a quantized Hall conductance in agreement with the analytical predictions. We also study the stability of the phase with respect to some of the experimentally relevant parameters
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
Topological d-wave pairing structures in Jain states
We discuss d-wave topological (broken time reversal symmetry) pairing
structures in unpolarized and polarized Jain states. We demonstrate pairing in
the Jain spin singlet state by rewriting it in an explicit pairing form, in
which we can recognize d-wave weak pairing of underlying quasiparticles -
neutral fermions. We find and describe the root configuration of the Jain spin
singlet state and its connection with neutral excitations of the Haldane-Rezayi
state, and study the transition between these states via exact diagonalization.
We find high overlaps with the Jain spin singlet state upon a departure from
the hollow core model for which the Haldane-Rezayi state is the exact ground
state. Due to a proven algebraic identity we were able to extend the analysis
of topological d-wave pairing structures to polarized Jain states and integer
quantum Hall states, and discuss its consequences.Comment: 8 page