384 research outputs found
Entanglement of purification: from spin chains to holography
Purification is a powerful technique in quantum physics whereby a mixed
quantum state is extended to a pure state on a larger system. This process is
not unique, and in systems composed of many degrees of freedom, one natural
purification is the one with minimal entanglement. Here we study the entropy of
the minimally entangled purification, called the entanglement of purification,
in three model systems: an Ising spin chain, conformal field theories
holographically dual to Einstein gravity, and random stabilizer tensor
networks. We conjecture values for the entanglement of purification in all
these models, and we support our conjectures with a variety of numerical and
analytical results. We find that such minimally entangled purifications have a
number of applications, from enhancing entanglement-based tensor network
methods for describing mixed states to elucidating novel aspects of the
emergence of geometry from entanglement in the AdS/CFT correspondence.Comment: 40 pages, multiple figures. v2: references added, typos correcte
Hidden Fermi surfaces in compressible states of gauge-gravity duality
General scaling arguments, and the behavior of the thermal entropy density,
are shown to lead to an infrared metric holographically representing a
compressible state with hidden Fermi surfaces. This metric is characterized by
a general dynamic critical exponent, z, and a specific hyperscaling violation
exponent, \theta. The same metric exhibits a logarithmic violation of the area
law of entanglement entropy, as shown recently by Ogawa et al.
(arXiv:1111.1023). We study the dependence of the entanglement entropy on the
shape of the entangling region(s), on the total charge density, on temperature,
and on the presence of additional visible Fermi surfaces of gauge-neutral
fermions; for the latter computations, we realize the needed metric in an
Einstein-Maxwell-dilaton theory. All our results support the proposal that the
holographic theory describes a metallic state with hidden Fermi surfaces of
fermions carrying gauge charges of deconfined gauge fields.Comment: 33 pages, 5 figures; (v2) added refs, corrected typos, and modified
figure; (v3) added table summarizing result
Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
We study a conjectured connection between the AdS/CFT and a real-space
quantum renormalization group scheme, the multi-scale entanglement
renormalization ansatz (MERA). By making a close contact with the holographic
formula of the entanglement entropy, we propose a general definition of the
metric in the MERA in the extra holographic direction, which is formulated
purely in terms of quantum field theoretical data. Using the continuum version
of the MERA (cMERA), we calculate this emergent holographic metric explicitly
for free scalar boson and free fermions theories, and check that the metric so
computed has the properties expected from AdS/CFT. We also discuss the cMERA in
a time-dependent background induced by quantum quench and estimate its
corresponding metric.Comment: 42pages, 9figures, reference added, minor chang
Large-density field theory, viscosity, and "" singularities from string duals
We analyze systems where an effective large-N expansion arises naturally in
gauge theories without a large number of colors: a sufficiently large charge
density alone can produce a perturbative string ('tHooft) expansion. One
example is simply the well-known NS5/F1 system dual to , here viewed as a 5+1 dimensional theory at finite density. This model is
completely stable, and we find that the existing string-theoretic solution of
this model yields two interesting results. First, it indicates that the shear
viscosity is not corrected by effects in this system. For flow
perpendicular to the F1 strings the viscosity to entropy ratio take the usual
value , but for flow parallel to the F1's it vanishes as at low
temperature. Secondly, it encodes singularities in correlation functions coming
from low-frequency modes at a finite value of the momentum along the
directions. This may provide a strong coupling analogue of finite density
condensed matter systems for which fermionic constituents of larger operators
contribute so-called "" singularities. In the NS5/F1 example, stretched
strings on the gravity side play the role of these composite operators. We
explore the analogue for our system of the Luttinger relation between charge
density and the volume bounded by these singular surfaces. This model provides
a clean example where the string-theoretic UV completion of the gravity dual to
a finite density field theory plays a significant and calculable role.Comment: 28 pages. v2: added reference
l-Threonine Deaminase of Rhodospirillum rubrum
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65547/1/j.1432-1033.1971.tb01490.x.pd
COMPUTER-CONTROLLED GAS CHROMATOGRAPH CAPABLE OF ''REAL-TIME'' READOUT OF HIGH-PRECISION DATA.
A gas chromatograph has been assembled which provides computer control of sample injection, column temperature, and flow rate, plus direct computer readout of inlet pressure, mass flow rate, and detector response. Data processing yields, in real-time, a standard deviation of less than 0.05% in retention time, which is comparable to previous results obtained using an off-line computer. However, corrected retention volumes determined in real-time had a standard deviation of about 0.4% which reflected primarily the uncertainty in flow measurement
Moduli Spaces of Cold Holographic Matter
We use holography to study (3+1)-dimensional N=4 supersymmetric Yang-Mills
theory with gauge group SU(Nc), in the large-Nc and large-coupling limits,
coupled to a single massless (n+1)-dimensional hypermultiplet in the
fundamental representation of SU(Nc), with n=3,2,1. In particular, we study
zero-temperature states with a nonzero baryon number charge density, which we
call holographic matter. We demonstrate that a moduli space of such states
exists in these theories, specifically a Higgs branch parameterized by the
expectation values of scalar operators bilinear in the hypermultiplet scalars.
At a generic point on the Higgs branch, the R-symmetry and gauge group are
spontaneously broken to subgroups. Our holographic calculation consists of
introducing a single probe Dp-brane into AdS5 times S^5, with p=2n+1=7,5,3,
introducing an electric flux of the Dp-brane worldvolume U(1) gauge field, and
then obtaining explicit solutions for the worldvolume fields dual to the scalar
operators that parameterize the Higgs branch. In all three cases, we can
express these solutions as non-singular self-dual U(1) instantons in a
four-dimensional space with a metric determined by the electric flux. We
speculate on the possibility that the existence of Higgs branches may point the
way to a counting of the microstates producing a nonzero entropy in holographic
matter. Additionally, we speculate on the possible classification of
zero-temperature, nonzero-density states described holographically by probe
D-branes with worldvolume electric flux.Comment: 56 pages, 8 PDF images, 4 figure
Entanglement Entropy from a Holographic Viewpoint
The entanglement entropy has been historically studied by many authors in
order to obtain quantum mechanical interpretations of the gravitational
entropy. The discovery of AdS/CFT correspondence leads to the idea of
holographic entanglement entropy, which is a clear solution to this important
problem in gravity. In this article, we would like to give a quick survey of
recent progresses on the holographic entanglement entropy. We focus on its
gravitational aspects, so that it is comprehensible to those who are familiar
with general relativity and basics of quantum field theory.Comment: Latex, 30 pages, invited review for Classical and Quantum Gravity,
minor correction
Luttinger's theorem, superfluid vortices, and holography
Strongly coupled field theories with gravity duals can be placed at finite
density in two ways: electric field flux emanating from behind a horizon, or
bulk charged fields outside of the horizon that explicitly source the density.
We discuss field-theoretical observables that are sensitive to this
distinction. If the charged fields are fermionic, we discuss a modified
Luttinger's theorem that holds for holographic systems, in which the sum of
boundary theory Fermi surfaces counts only the charge outside of the horizon.
If the charged fields are bosonic, we show that the the resulting superfluid
phase may be characterized by the coefficient of the transverse Magnus force on
a moving superfluid vortex, which again is sensitive only to the charge outside
of the horizon. For holographic systems these observables provide a
field-theoretical way to distinguish how much charge is held by a dual horizon,
but they may be useful in more general contexts as measures of deconfined (i.e.
"fractionalized") charge degrees of freedom.Comment: 21 pages; version 2: minor changes, version to be published in CQG;
version 3: minor change
Boundary States as Holographic Duals of Trivial Spacetimes
We study real-space quantum entanglement included in conformally invariant
boundary states in conformal field theories (CFTs). First, we argue that
boundary states essentially have no real-space entanglement by computing the
entanglement entropy when we bipartite the system into two spatial regions.
From the viewpoint of holography, this shows that boundary states are dual to
trivial spacetimes of zero spactime volume. Next, we point out that a
continuous multiscale entanglement renormalization ansatz (cMERA) for any CFTs
can be formulated by employing a boundary state as its infrared unentangled
state with an appropriate regularization. Exploiting this idea, we propose an
approximation scheme of cMERA construction for general CFTs.Comment: 30 pages, 4 figure
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