86 research outputs found
Quantum Hall Circle
We consider spin-polarized electrons in a single Landau level on a cylinder
as the circumference of the cylinder goes to infinity. This gives a model of
interacting electrons on a circle where the momenta of the particles are
restricted and there is no kinetic energy. Quantum Hall states are exact ground
states for appropriate short range interactions, and there is a gap to
excitations. These states develop adiabatically from this one-dimensional
quantum Hall circle to the bulk quantum Hall states and further on into the
Tao-Thouless states as the circumference goes to zero. For low filling
fractions a gapless state is formed which we suggest is connected to the Wigner
crystal expected in the bulk.Comment: 12 pages, publishe
The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
We analyze the Moore-Read Pfaffian state on a thin torus. The known six-fold
degeneracy is realized by two inequivalent crystalline states with a four- and
two-fold degeneracy respectively. The fundamental quasihole and quasiparticle
excitations are domain walls between these vacua, and simple counting arguments
give a Hilbert space of dimension for holes and particles
at fixed positions and assign each a charge . This generalizes the
known properties of the hole excitations in the Pfaffian state as deduced using
conformal field theory techniques. Numerical calculations using a model
hamiltonian and a small number of particles supports the presence of a stable
phase with degenerate vacua and quarter charged domain walls also away from the
thin torus limit. A spin chain hamiltonian encodes the degenerate vacua and the
various domain walls.Comment: 4 pages, 1 figure. Published, minor change
Topological insulators with arbitrarily tunable entanglement
We elucidate how Chern and topological insulators fulfill an area law for the
entanglement entropy. By explicit construction of a family of lattice
Hamiltonians, we are able to demonstrate that the area law contribution can be
tuned to an arbitrarily small value, but is topologically protected from
vanishing exactly. We prove this by introducing novel methods to bound
entanglement entropies from correlations using perturbation bounds, drawing
intuition from ideas of quantum information theory. This rigorous approach is
complemented by an intuitive understanding in terms of entanglement edge
states. These insights have a number of important consequences: The area law
has no universal component, no matter how small, and the entanglement scaling
cannot be used as a faithful diagnostic of topological insulators. This holds
for all Renyi entropies which uniquely determine the entanglement spectrum
which is hence also non-universal. The existence of arbitrarily weakly
entangled topological insulators furthermore opens up possibilities of devising
correlated topological phases in which the entanglement entropy is small and
which are thereby numerically tractable, specifically in tensor network
approaches.Comment: 9 pages, 3 figures, final versio
Composite symmetry protected topological order and effective models
Strongly correlated quantum many-body systems at low dimension exhibit a
wealth of phenomena, ranging from features of geometric frustration to
signatures of symmetry-protected topological order. In suitable descriptions of
such systems, it can be helpful to resort to effective models which focus on
the essential degrees of freedom of the given model. In this work, we analyze
how to determine the validity of an effective model by demanding it to be in
the same phase as the original model. We focus our study on one-dimensional
spin-1/2 systems and explain how non-trivial symmetry protected topologically
ordered (SPT) phases of an effective spin 1 model can arise depending on the
couplings in the original Hamiltonian. In this analysis, tensor network methods
feature in two ways: On the one hand, we make use of recent techniques for the
classification of SPT phases using matrix product states in order to identify
the phases in the effective model with those in the underlying physical system,
employing Kuenneth's theorem for cohomology. As an intuitive paradigmatic model
we exemplify the developed methodology by investigating the bi-layered
delta-chain. For strong ferromagnetic inter-layer couplings, we find the system
to transit into exactly the same phase as an effective spin 1 model. However,
for weak but finite coupling strength, we identify a symmetry broken phase
differing from this effective spin-1 description. On the other hand, we
underpin our argument with a numerical analysis making use of matrix product
states.Comment: 13 pages, 6 figure
Symmetry Breaking on the Three-Dimensional Hyperkagome Lattice of Na_4Ir_3O_8
We study the antiferromagnetic spin-1/2 Heisenberg model on the highly
frustrated, three-dimensional, hyperkagome lattice of Na_4Ir_3O_8 using a
series expansion method. We propose a valence bond crystal with a 72 site unit
cell as a ground state that supports many, very low lying, singlet excitations.
Low energy spinons and triplons are confined to emergent lower-dimensional
motifs. Here, and for analogous kagome and pyrochlore states, we suggest finite
temperature signatures, including an Ising transition, in the magnetic specific
heat due to a multistep breaking of discrete symmetries.Comment: 4 pages, 3 figure
Hierarchy wave functions--from conformal correlators to Tao-Thouless states
Laughlin's wave functions, describing the fractional quantum Hall effect at
filling factors , can be obtained as correlation functions in
conformal field theory, and recently this construction was extended to Jain's
composite fermion wave functions at filling factors . Here we
generalize this latter construction and present ground state wave functions for
all quantum Hall hierarchy states that are obtained by successive condensation
of quasielectrons (as opposed to quasiholes) in the original hierarchy
construction. By considering these wave functions on a cylinder, we show that
they approach the exact ground states, the Tao-Thouless states, when the
cylinder becomes thin. We also present wave functions for the multi-hole
states, make the connection to Wen's general classification of abelian quantum
Hall fluids, and discuss whether the fractional statistics of the
quasiparticles can be analytically determined. Finally we discuss to what
extent our wave functions can be described in the language of composite
fermions.Comment: 9 page
Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators
We show that, quite generically, a [111] slab of spin-orbit coupled
pyrochlore lattice exhibits surface states whose constant energy curves take
the shape of Fermi arcs, localized to different surfaces depending on their
quasimomentum. Remarkably, these persist independently of the existence of Weyl
points in the bulk. Considering interacting electrons in slabs of finite
thickness, we find a plethora of known fractional Chern insulating phases, to
which we add the discovery of a new higher Chern number state which is likely a
generalization of the Moore-Read fermionic fractional quantum Hall state. By
contrast, in the three-dimensional limit, we argue for the absence of gapped
states of the flat surface band due to a topologically protected coupling of
the surface to gapless states in the bulk. We comment on generalizations as
well as experimental perspectives in thin slabs of pyrochlore iridates.Comment: Published. 6+4 page
Microscopic theory of the quantum Hall hierarchy
We solve the quantum Hall problem exactly in a limit and show that the ground
states can be organized in a fractal pattern consistent with the
Haldane-Halperin hierarchy, and with the global phase diagram. We present wave
functions for a large family of states, including those of Laughlin and Jain
and also for states recently observed by Pan {\it et. al.}, and show that they
coincide with the exact ones in the solvable limit. We submit that they
establish an adiabatic continuation of our exact results to the experimentally
accessible regime, thus providing a unified approach to the hierarchy states.Comment: 4 pages, 2 figures. Publishe
Hierarchy of fractional Chern insulators and competing compressible states
We study the phase diagram of interacting electrons in a dispersionless Chern
band as a function of their filling. We find hierarchy multiplets of
incompressible states at fillings \nu=1/3, 2/5, 3/7, 4/9, 5/9, 4/7, 3/5 as well
as \nu=1/5,2/7. These are accounted for by an analogy to Haldane
pseudopotentials extracted from an analysis of the two-particle problem.
Important distinctions to standard fractional quantum Hall physics are
striking: absent particle-hole symmetry in a single band, an
interaction-induced single-hole dispersion appears, which perturbs and
eventually destabilizes incompressible states as \nu increases. For this reason
the nature of the state at \nu=2/3 is hard to pin down, while \nu=5/7,4/5 do
not seem to be incompressible in our system.Comment: 5 pages with 4 figures, plus 6 pages and 8 figures of supplementary
materia
Half-Filled Lowest Landau Level on a Thin Torus
We solve a model that describes an interacting electron gas in the
half-filled lowest Landau level on a thin torus, with radius of the order of
the magnetic length. The low energy sector consists of non-interacting,
one-dimensional, neutral fermions. The ground state, which is homogeneous, is
the Fermi sea obtained by filling the negative energy states and the excited
states are gapless neutral excitations out of this one-dimensional sea.
Although the limit considered is extreme, the solution has a striking
resemblance to the composite fermion description of the bulk
state--the ground state is homogeneous and the excitations are neutral and
gapless. This suggests a one-dimensional Luttinger liquid description, with
possible observable effects in transport experiments, of the bulk state where
it develops continuously from the state on a thin torus as the radius
increases.Comment: 4 pages, 1 figur
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