71 research outputs found
Dynamical Topological Quantum Phase Transitions for Mixed States
We introduce and study dynamical probes of band structure topology in the
post-quench time-evolution from mixed initial states of quantum many-body
systems. Our construction generalizes the notion of dynamical quantum phase
transitions (DQPTs), a real-time counterpart of conventional equilibrium phase
transitions in quantum dynamics, to finite temperatures and generalized Gibbs
ensembles. The non-analytical signatures hallmarking these mixed state DQPTs
are found to be characterized by observable phase singularities manifesting in
the dynamical formation of vortex-antivortex pairs in the interferometric phase
of the density matrix. Studying quenches in Chern insulators, we find that
changes in the topological properties of the Hamiltonian can be identified in
this scenario, without ever preparing a topologically non-trivial or
low-temperature initial state. Our observations are of immediate relevance for
current experiments aimed at realizing topological phases in ultracold atomic
gases.Comment: 4 pages, 3 figures, version close to publishe
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
Synthetic Helical Liquids with Ultracold Atoms in Optical Lattices
We discuss a platform for the synthetic realization of key physical
properties of helical Tomonaga Luttinger liquids (HTLLs) with ultracold
fermionic atoms in one-dimensional optical lattices. The HTLL is a strongly
correlated metallic state where spin polarization and propagation direction of
the itinerant particles are locked to each other. We propose an unconventional
one-dimensional Fermi-Hubbard model which, at quarter filling, resembles the
HTLL in the long wavelength limit, as we demonstrate with a combination of
analytical (bosonization) and numerical (density matrix renormalization group)
methods. An experimentally feasible scheme is provided for the realization of
this model with ultracold fermionic atoms in optical lattices. Finally, we
discuss how the robustness of the HTLL against back-scattering and
imperfections, well known from its realization at the edge of two-dimensional
topological insulators, is reflected in the synthetic one-dimensional scenario
proposed here
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
Tunable quantum spin Hall effect in double quantum wells
The field of topological insulators (TIs) is rapidly growing. Concerning
possible applications, the search for materials with an easily controllable TI
phase is a key issue. The quantum spin Hall effect, characterized by a single
pair of helical edge modes protected by time-reversal symmetry, has been
demonstrated in HgTe-based quantum wells (QWs) with an inverted bandgap. We
analyze the topological properties of a generically coupled HgTe-based double
QW (DQW) and show how in such a system a TI phase can be driven by an
inter-layer bias voltage, even when the individual layers are non-inverted. We
argue, that this system allows for similar (layer-)pseudospin based physics as
in bilayer graphene but with the crucial absence of a valley degeneracy.Comment: 9 pages, 8 figures, extended version (accepted Phys. Rev. B
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