3,780 research outputs found
Holographic Entanglement Entropy
We review the developments in the past decade on holographic entanglement
entropy, a subject that has garnered much attention owing to its potential to
teach us about the emergence of spacetime in holography. We provide an
introduction to the concept of entanglement entropy in quantum field theories,
review the holographic proposals for computing the same, providing some
justification for where these proposals arise from in the first two parts. The
final part addresses recent developments linking entanglement and geometry. We
provide an overview of the various arguments and technical developments that
teach us how to use field theory entanglement to detect geometry. Our
discussion is by design eclectic; we have chosen to focus on developments that
appear to us most promising for further insights into the holographic map.
This is a draft of a few chapters of a book which will appear sometime in the
near future, to be published by Springer. The book in addition contains a
discussion of application of holographic ideas to computation of entanglement
entropy in strongly coupled field theories, and discussion of tensor networks
and holography, which we have chosen to exclude from the current manuscript.Comment: 154 pages. many figures. preliminary version of book chapters.
comments welcome. v2: typos fixed and references adde
Axiomatic Attribution for Multilinear Functions
We study the attribution problem, that is, the problem of attributing a
change in the value of a characteristic function to its independent variables.
We make three contributions. First, we propose a formalization of the problem
based on a standard cost sharing model. Second, we show that there is a unique
attribution method that satisfies Dummy, Additivity, Conditional Nonnegativity,
Affine Scale Invariance, and Anonymity for all characteristic functions that
are the sum of a multilinear function and an additive function. We term this
the Aumann-Shapley-Shubik method. Conversely, we show that such a uniqueness
result does not hold for characteristic functions outside this class. Third, we
study multilinear characteristic functions in detail; we describe a
computationally efficient implementation of the Aumann-Shapley-Shubik method
and discuss practical applications to pay-per-click advertising and portfolio
analysis.Comment: 21 pages, 2 figures, updated version for EC '1
Entanglement structures in qubit systems
Using measures of entanglement such as negativity and tangles we provide a
detailed analysis of entanglement structures in pure states of non-interacting
qubits. The motivation for this exercise primarily comes from holographic
considerations, where entanglement is inextricably linked with the emergence of
geometry. We use the qubit systems as toy models to probe the internal
structure, and introduce some useful measures involving entanglement negativity
to quantify general features of entanglement. In particular, our analysis
focuses on various constraints on the pattern of entanglement which are known
to be satisfied by holographic sates, such as the saturation of Araki-Lieb
inequality (in certain circumstances), and the monogamy of mutual information.
We argue that even systems as simple as few non-interacting qubits can be
useful laboratories to explore how the emergence of the bulk geometry may be
related to quantum information principles.Comment: 55 pages, 23 figures. v2: typos fixed. v3: minor clarifications.
published versio
D-brane Dynamics and the Quantum Hall Effect
We study the recently proposed D-brane configuration [hep-th/0010105]
modeling the quantum Hall effect, focusing on the nature of the interactions
between the charged particles. Our analysis indicates that the interaction is
repulsive, which it should be for the ground state of the system to behave as a
quantum Hall liquid. The strength of interactions varies inversely with the
filling fraction, leading us to conclude that a Wigner crystal is the ground
state at small nu. For larger rational nu (still less than unity), it is
reasonable to expect a fractional quantum Hall ground state.Comment: 13 pages, latex, two figures. v2: Corrected cyclotron gap makes
quantum Hall ground state more likel
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