477 research outputs found
Effective One-Dimensional Models from Matrix Product States
In this paper we present a method for deriving effective one-dimensional
models based on the matrix product state formalism. It exploits translational
invariance to work directly in the thermodynamic limit. We show, how a
representation of the creation operator of single quasi-particles in both real
and momentum space can be extracted from the dispersion calculation. The method
is tested for the analytically solvable Ising model in a transverse magnetic
field. Properties of the matrix product representation of the creation operator
are discussed and validated by calculating the one-particle contribution to the
spectral weight. Results are also given for the ground state energy and the
dispersion.Comment: 17 pages, 8 figure
Quantum kinetic Ising models
We introduce a quantum generalization of classical kinetic Ising models,
described by a certain class of quantum many body master equations. Similarly
to kinetic Ising models with detailed balance that are equivalent to certain
Hamiltonian systems, our models reduce to a set of Hamiltonian systems
determining the dynamics of the elements of the many body density matrix. The
ground states of these Hamiltonians are well described by matrix product, or
pair entangled projected states. We discuss critical properties of such
Hamiltonians, as well as entanglement properties of their low energy states.Comment: 20 pages, 4 figures, minor improvements, accepted in New Journal of
Physic
Entanglement and energy level crossing of spin and Fermi Hamilton operators
M.Sc. (Applied Mathematics)Entanglement is a quantum resource with applications in quantum communication as well as quantum computing amongst others. Since quantum entanglement is such an abstract concept numerous mathematical measures exist. Some of these have a purely theoretic purpose whereas others play a role in describing the magnitude of entanglement of a system. In quantum systems energy level crossing may occur. Energy levels in quantum systems tend to repel each other so when any type of degeneracy occurs where the energy levels coalesce or cross it is of interest to us. Two such points of degeneracy are exceptional and diabolic points. When these occur it is useful to investigate these points in specific systems and observe level crossing. In this thesis we mainly investigate the relationship between entanglement, energy level crossing and symmetry as well as the exceptional and diabolic points of specific systems. We are especially interested in systems described by spin and Fermi operators
Detection of multipartite entanglement in the vicinity of symmetric Dicke states
We present methods for detecting entanglement around symmetric Dicke states.
In particular, we consider N-qubit symmetric Dicke states with N/2 excitations.
In the first part of the paper we show that for large N these states have the
smallest overlap possible with states without genuine multi-partite
entanglement. Thus these states are particulary well suited for the
experimental examination of multi-partite entanglement. We present
fidelity-based entanglement witness operators for detecting multipartite
entanglement around these states. In the second part of the paper we consider
entanglement criteria, somewhat similar to the spin squeezing criterion, based
on the moments or variances of the collective spin operators. Surprisingly,
these criteria are based on an upper bound for variances for separable states.
We present both criteria detecting entanglement in general and criteria
detecting only genuine multi-partite entanglement. The collective operator
measured for our criteria is an important physical quantity: Its expectation
value essentially gives the intensity of the radiation when a coherent atomic
cloud emits light.Comment: 8 pages, no figures, revtex4; typos corrected, presentation improved,
part about connection to superradiance added; published version; J. Opt. Soc.
Am. B, Feature issue on optical quantum information science, Eds. B. Sanders,
A. Zeilinger, and Y. Yamamot
Quantum Hamiltonian Complexity
Constraint satisfaction problems are a central pillar of modern computational
complexity theory. This survey provides an introduction to the rapidly growing
field of Quantum Hamiltonian Complexity, which includes the study of quantum
constraint satisfaction problems. Over the past decade and a half, this field
has witnessed fundamental breakthroughs, ranging from the establishment of a
"Quantum Cook-Levin Theorem" to deep insights into the structure of 1D
low-temperature quantum systems via so-called area laws. Our aim here is to
provide a computer science-oriented introduction to the subject in order to
help bridge the language barrier between computer scientists and physicists in
the field. As such, we include the following in this survey: (1) The
motivations and history of the field, (2) a glossary of condensed matter
physics terms explained in computer-science friendly language, (3) overviews of
central ideas from condensed matter physics, such as indistinguishable
particles, mean field theory, tensor networks, and area laws, and (4) brief
expositions of selected computer science-based results in the area. For
example, as part of the latter, we provide a novel information theoretic
presentation of Bravyi's polynomial time algorithm for Quantum 2-SAT.Comment: v4: published version, 127 pages, introduction expanded to include
brief introduction to quantum information, brief list of some recent
developments added, minor changes throughou
A variational method based on weighted graph states
In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a
class of states which is suitable as a variational set to find ground states in
spin systems of arbitrary spatial dimension and with long-range entanglement.
Here, we continue the exposition of our technique, extend from spin 1/2 to
higher spins and use the boson Hubbard model as a non-trivial example to
demonstrate our scheme.Comment: 36 pages, 13 figure
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