12 research outputs found
Geometric Aspects of Holographic Bit Threads
We revisit the recent reformulation of the holographic prescription to
compute entanglement entropy in terms of a convex optimization problem,
introduced by Freedman and Headrick. According to it, the holographic
entanglement entropy associated to a boundary region is given by the maximum
flux of a bounded, divergenceless vector field, through the corresponding
region. Our work leads to two main results: (i) We present a general algorithm
that allows the construction of explicit thread configurations in cases where
the minimal surface is known. We illustrate the method with simple examples:
spheres and strips in vacuum AdS, and strips in a black brane geometry.
Studying more generic bulk metrics, we uncover a sufficient set of conditions
on the geometry and matter fields that must hold to be able to use our
prescription. (ii) Based on the nesting property of holographic entanglement
entropy, we develop a method to construct bit threads that maximize the flux
through a given bulk region. As a byproduct, we are able to construct more
general thread configurations by combining (i) and (ii) in multiple patches. We
apply our methods to study bit threads which simultaneously compute the
entanglement entropy and the entanglement of purification of mixed states and
comment on their interpretation in terms of entanglement distillation. We also
consider the case of disjoint regions for which we can explicitly construct the
so-called multi-commodity flows and show that the monogamy property of mutual
information can be easily illustrated from our constructions.Comment: 48 pages, multiple figures. v3: matches published versio
Large distance expansion of Mutual Information for disjoint disks in a free scalar theory
We compute the next-to-leading order term in the long-distance expansion of
the mutual information for free scalars in three space-time dimensions. The
geometry considered is two disjoint disks separated by a distance between
their centers. No evidence for non-analyticity in the R\'enyi parameter for
the continuation in the next-to-leading order term is found.Comment: 15 pages, This version contains few extra references, some technical
material has been move to appendices, and other minor modifications to match
with the version accepted for publicatio
R\'enyi entropies in the limit and entanglement temperatures
Entanglement temperatures (ET) are a generalization of Unruh temperatures
valid for states reduced to any region of space. They encode in a thermal
fashion the high energy behavior of the state around a point. These
temperatures are determined by an eikonal equation in Euclidean space. We show
that the real-time continuation of these equations implies ballistic
propagation. For theories with a free UV fixed point, the ET determines the
state at a large modular temperature. In particular, we show that the
limit of R\'enyi entropies , can be computed from the ET. This establishes
a formula for these R\'enyi entropies for any region in terms of solutions of
the eikonal equations. In the limit, the relevant high-temperature
state propagation is determined by a free relativistic Boltzmann equation, with
an infinite tower of conserved currents. For the special case of states and
regions with a conformal Killing symmetry, these equations coincide with the
ones of a perfect fluid.Comment: 33 pages, 3 figure
Bit Threads and the Membrane Theory of Entanglement Dynamics
Recently, an effective {\it membrane theory} was proposed that describes the
``hydrodynamic'' regime of the entanglement dynamics for general chaotic
systems. Motivated by the new {\it bit threads} formulation of holographic
entanglement entropy, given in terms of a convex optimization problem based on
flow maximization, or equivalently tight packing of bit threads, we reformulate
the membrane theory as a max flow problem by proving a max flow-min cut
theorem. In the context of holography, we explain the relation between the max
flow program dual to the membrane theory and the max flow program dual to the
holographic surface extremization prescription by providing an explicit map
from the membrane to the bulk, and derive the former from the latter in the
``hydrodynamic'' regime without reference to minimal surfaces or membranes.Comment: 31 pages, 8 figures; v2: Improved figures, references added, a new
discussion section was included, matches the published versio
Rényi entropies in the n →0 limit and entanglement temperatures
Entanglement temperatures (ET) are a generalization of Unruh temperatures valid for states reduced to any region of space. They encode in a thermal fashion the high energy behavior of the state around a point. These temperatures are determined by an eikonal equation in Euclidean space. We show that the real-time continuation of these equations implies ballistic propagation. For theories with a free UV fixed point, the ET determines the state at a large modular temperature. In particular, we show that the n→0 limit of Rényi entropies Sn, can be computed from the ET. This establishes a formula for these Rényi entropies for any region in terms of solutions of the eikonal equations. In the n→0 limit, the relevant high-temperature state propagation is determined by a free relativistic Boltzmann equation, with an infinite tower of conserved currents. For the special case of states and regions with a conformal Killing symmetry, these equations coincide with the ones of a perfect fluid.Fil: Agón, Cesar A.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Martinez, Pedro Jorge. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin