6,966 research outputs found
Holographic Shear Viscosity in Hyperscaling Violating Theories without Translational Invariance
In this paper we investigate the ratio of shear viscosity to entropy density,
, 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,
. We find the exponent 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 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
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
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
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
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
- …