1,526 research outputs found
Area law violations in a supersymmetric model
We study the structure of entanglement in a supersymmetric lattice model of
fermions on certain types of decorated graphs with quenched disorder. In
particular, we construct models with controllable ground state degeneracy
protected by supersymmetry and the choice of Hilbert space. We show that in
certain special limits these degenerate ground states are associated with local
impurities and that there exists a basis of the ground state manifold in which
every basis element satisfies a boundary law for entanglement entropy. On the
other hand, by considering incoherent mixtures or coherent superpositions of
these localized ground states, we can find regions that violate the boundary
law for entanglement entropy over a wide range of length scales. More
generally, we discuss various desiderata for constructing violations of the
boundary law for entanglement entropy and discuss possible relations of our
work to recent holographic studies.Comment: 20 pages, 1 figure, 1 appendi
Functionality in single-molecule devices: Model calculations and applications of the inelastic electron tunneling signal in molecular junctions
We analyze how functionality could be obtained within single-molecule devices
by using a combination of non-equilibrium Green's functions and ab-initio
calculations to study the inelastic transport properties of single-molecule
junctions. First we apply a full non-equilibrium Green's function technique to
a model system with electron-vibration coupling. We show that the features in
the inelastic electron tunneling spectra (IETS) of the molecular junctions are
virtually independent of the nature of the molecule-lead contacts. Since the
contacts are not easily reproducible from one device to another, this is a very
useful property. The IETS signal is much more robust versus modifications at
the contacts and hence can be used to build functional nanodevices. Second, we
consider a realistic model of a organic conjugated molecule. We use ab-initio
calculations to study how the vibronic properties of the molecule can be
controlled by an external electric field which acts as a gate voltage. The
control, through the gate voltage, of the vibron frequencies and (more
importantly) of the electron-vibron coupling enables the construction of
functionality: non-linear amplification and/or switching is obtained from the
IETS signal within a single-molecule device.Comment: Accepted for publication in Journal of Chemical Physic
Faster Methods for Contracting Infinite 2D Tensor Networks
We revisit the corner transfer matrix renormalization group (CTMRG) method of
Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and
demonstrate that its performance can be substantially improved by determining
the tensors using an eigenvalue solver as opposed to the power method used in
CTMRG. We also generalize the variational uniform matrix product state (VUMPS)
ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer
matrices and discuss similarities with the corner methods. These two new
algorithms will be crucial to improving the performance of variational infinite
projected entangled pair state (PEPS) methods.Comment: 20 pages, 5 figures, V. Zauner-Stauber previously also published
under the name V. Zaune
Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
We develop variational matrix product state (MPS) methods with symmetries to
determine dispersion relations of one dimensional quantum lattices as a
function of momentum and preset quantum number. We test our methods on the XXZ
spin chain, the Hubbard model and a non-integrable extended Hubbard model, and
determine the excitation spectra with a precision similar to the one of the
ground state. The formulation in terms of quantum numbers makes the topological
nature of spinons and holons very explicit. In addition, the method also
enables an easy and efficient direct calculation of the necessary magnetic
field or chemical potential required for a certain ground state magnetization
or particle density.Comment: 13 pages, 4 pages appendix, 8 figure
The Algebraic Bethe Ansatz and Tensor Networks
We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ
Heisenberg chains with open and periodic boundary conditions in terms of tensor
networks. These Bethe eigenstates have the structure of Matrix Product States
with a conserved number of down-spins. The tensor network formulation suggestes
possible extensions of the Algebraic Bethe Ansatz to two dimensions
Thermal States as Convex Combinations of Matrix Product States
We study thermal states of strongly interacting quantum spin chains and prove
that those can be represented in terms of convex combinations of matrix product
states. Apart from revealing new features of the entanglement structure of
Gibbs states our results provide a theoretical justification for the use of
White's algorithm of minimally entangled typical thermal states. Furthermore,
we shed new light on time dependent matrix product state algorithms which yield
hydrodynamical descriptions of the underlying dynamics.Comment: v3: 10 pages, 2 figures, final published versio
Binegativity and geometry of entangled states in two qubits
We prove that the binegativity is always positive for any two-qubit state. As
a result, as suggested by the previous works, the asymptotic relative entropy
of entanglement in two qubits does not exceed the Rains bound, and the
PPT-entanglement cost for any two-qubit state is determined to be the
logarithmic negativity of the state. Further, the proof reveals some
geometrical characteristics of the entangled states, and shows that the partial
transposition can give another separable approximation of the entangled state
in two qubits.Comment: 5 pages, 3 figures. I made the proof more transparen
Renormalization algorithm with graph enhancement
We introduce a class of variational states to describe quantum many-body
systems. This class generalizes matrix product states which underly the
density-matrix renormalization group approach by combining them with weighted
graph states. States within this class may (i) possess arbitrarily long-ranged
two-point correlations, (ii) exhibit an arbitrary degree of block entanglement
entropy up to a volume law, (iii) may be taken translationally invariant, while
at the same time (iv) local properties and two-point correlations can be
computed efficiently. This new variational class of states can be thought of as
being prepared from matrix product states, followed by commuting unitaries on
arbitrary constituents, hence truly generalizing both matrix product and
weighted graph states. We use this class of states to formulate a
renormalization algorithm with graph enhancement (RAGE) and present numerical
examples demonstrating that improvements over density-matrix renormalization
group simulations can be achieved in the simulation of ground states and
quantum algorithms. Further generalizations, e.g., to higher spatial
dimensions, are outlined.Comment: 4 pages, 1 figur
Edge theories in Projected Entangled Pair State models
We study the edge physics of gapped quantum systems in the framework of
Projected Entangled Pair State (PEPS) models. We show that the effective
low-energy model for any region acts on the entanglement degrees of freedom at
the boundary, corresponding to physical excitations located at the edge. This
allows us to determine the edge Hamiltonian in the vicinity of PEPS models, and
we demonstrate that by choosing the appropriate bulk perturbation, the edge
Hamiltonian can exhibit a rich phase diagram and phase transitions. While for
models in the trivial phase any Hamiltonian can be realized at the edge, we
show that for topological models, the edge Hamiltonian is constrained by the
topological order in the bulk which can e.g. protect a ferromagnetic Ising
chain at the edge against spontaneous symmetry breaking.Comment: 5 pages, 4 figure
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