6,966 research outputs found

    Holographic Shear Viscosity in Hyperscaling Violating Theories without Translational Invariance

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    In this paper we investigate the ratio of shear viscosity to entropy density, η/s\eta/s, in hyperscaling violating geometry with lattice structure. We show that the scaling relation with hyperscaling violation gives a strong constraint to the mass of graviton and usually leads to a power law of temperature, η/sTκ\eta/s\sim T^\kappa. We find the exponent κ\kappa can be greater than two such that the new bound for viscosity raised in arXiv:1601.02757 is violated. Our above observation is testified by constructing specific solutions with UV completion in various holographic models. Finally, we compare the boundedness of κ\kappa with the behavior of entanglement entropy and conjecture a relation between them.Comment: 38 pages, 8 figures: 1 appendix added, 2 figures added, 1 references adde

    Positive Entropy Invariant Measures on the Space of Lattices with Escape of Mass

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    On the space of unimodular lattices, we construct a sequence of invariant probability measures under a singular diagonal element with high entropy and show that the limit measure is 0

    Entanglement rates and the stability of the area law for the entanglement entropy

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    We prove a conjecture by Bravyi on an upper bound on entanglement rates of local Hamiltonians. We then use this bound to prove the stability of the area law for the entanglement entropy of quantum spin systems under adiabatic and quasi-adiabatic evolutions

    Invariant measures and the set of exceptions to Littlewood's conjecture

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    We classify the measures on SL (k,R)/SL (k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood's conjecture has Hausdorff dimension zero.Comment: 48 page

    Bose-Fermi duality and entanglement entropies

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    Entanglement (Renyi) entropies of spatial regions are a useful tool for characterizing the ground states of quantum field theories. In this paper we investigate the extent to which these are universal quantities for a given theory, and to which they distinguish different theories, by comparing the entanglement spectra of the massless Dirac fermion and the compact free boson in two dimensions. We show that the calculation of Renyi entropies via the replica trick for any orbifold theory includes a sum over orbifold twists on all cycles. In a modular-invariant theory of fermions, this amounts to a sum over spin structures. The result is that the Renyi entropies respect the standard Bose-Fermi duality. Next, we investigate the entanglement spectrum for the Dirac fermion without a sum over spin structures, and for the compact boson at the self-dual radius. These are not equivalent theories; nonetheless, we find that (1) their second Renyi entropies agree for any number of intervals, (2) their full entanglement spectra agree for two intervals, and (3) the spectrum generically disagrees otherwise. These results follow from the equality of the partition functions of the two theories on any Riemann surface with imaginary period matrix. We also exhibit a map between the operators of the theories that preserves scaling dimensions (but not spins), as well as OPEs and correlators of operators placed on the real line. All of these coincidences can be traced to the fact that the momentum lattice for the bosonized fermion is related to that of the self-dual boson by a 45 degree rotation that mixes left- and right-movers.Comment: 40 pages; v3: improvements to presentation, new section discussing entanglement negativit
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