7,643 research outputs found
Entanglement entropy of two disjoint intervals in c=1 theories
We study the scaling of the Renyi entanglement entropy of two disjoint blocks
of critical lattice models described by conformal field theories with central
charge c=1. We provide the analytic conformal field theory result for the
second order Renyi entropy for a free boson compactified on an orbifold
describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual
line. We have checked this prediction in cluster Monte Carlo simulations of the
classical two dimensional AT model. We have also performed extensive numerical
simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor
network techniques that allowed to obtain the reduced density matrices of
disjoint blocks of the spin-chain and to check the correctness of the
predictions for Renyi and entanglement entropies from conformal field theory.
In order to match these predictions, we have extrapolated the numerical results
by properly taking into account the corrections induced by the finite length of
the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure
The asymptotic spectrum of graphs and the Shannon capacity
We introduce the asymptotic spectrum of graphs and apply the theory of
asymptotic spectra of Strassen (J. Reine Angew. Math. 1988) to obtain a new
dual characterisation of the Shannon capacity of graphs. Elements in the
asymptotic spectrum of graphs include the Lov\'asz theta number, the fractional
clique cover number, the complement of the fractional orthogonal rank and the
fractional Haemers bounds
Confinement and Condensates Without Fine Tuning in Supergravity Duals of Gauge Theories
We discuss a solution of the equations of motion of five-dimensional gauged
type IIB supergravity that describes confining SU(N) gauge theories at large N
and large 't Hooft parameter. We prove confinement by computing the Wilson
loop, and we show that our solution is generic, independent of most of the
details of the theory. In particular, the Einstein-frame metric near its
singularity, and the condensates of scalar, composite operators are universal.
Also universal is the discreteness of the glueball mass spectrum and the
existence of a mass gap. The metric is also identical to a generically
confining solution recently found in type 0B theory.Comment: 19 pages, Late
Covariant techniques for computation of the heat kernel
The heat kernel associated with an elliptic second-order partial differential
operator of Laplace type acting on smooth sections of a vector bundle over a
Riemannian manifold, is studied. A general manifestly covariant method for
computation of the coefficients of the heat kernel asymptotic expansion is
developed. The technique enables one to compute explicitly the diagonal values
of the heat kernel coefficients, so called Hadamard-Minackshisundaram-De
Witt-Seeley coefficients, as well as their derivatives. The elaborated
technique is applicable for a manifold of arbitrary dimension and for a generic
Riemannian metric of arbitrary signature. It is very algorithmic, and well
suited to automated computation. The fourth heat kernel coefficient is computed
explicitly for the first time. The general structure of the heat kernel
coefficients is investigated in detail. On the one hand, the leading derivative
terms in all heat kernel coefficients are computed. On the other hand, the
generating functions in closed covariant form for the covariantly constant
terms and some low-derivative terms in the heat kernel coefficients are
constructed by means of purely algebraic methods. This gives, in particular,
the whole sequence of heat kernel coefficients for an arbitrary locally
symmetric space.Comment: 31 pages, LaTeX, no figures, Invited Lecture at the University of
Iowa, Iowa City, April, 199
The asymptotic spectrum of LOCC transformations
We study exact, non-deterministic conversion of multipartite pure quantum
states into one-another via local operations and classical communication (LOCC)
and asymptotic entanglement transformation under such channels. In particular,
we consider the maximal number of copies of any given target state that can be
extracted exactly from many copies of any given initial state as a function of
the exponential decay in success probability, known as the converese error
exponent. We give a formula for the optimal rate presented as an infimum over
the asymptotic spectrum of LOCC conversion. A full understanding of exact
asymptotic extraction rates between pure states in the converse regime thus
depends on a full understanding of this spectrum. We present a characterisation
of spectral points and use it to describe the spectrum in the bipartite case.
This leads to a full description of the spectrum and thus an explicit formula
for the asymptotic extraction rate between pure bipartite states, given a
converse error exponent. This extends the result on entanglement concentration
in [Hayashi et al, 2003], where the target state is fixed as the Bell state. In
the limit of vanishing converse error exponent the rate formula provides an
upper bound on the exact asymptotic extraction rate between two states, when
the probability of success goes to 1. In the bipartite case we prove that this
bound holds with equality.Comment: v1: 21 pages v2: 21 pages, Minor corrections v3: 17 pages, Minor
corrections, new reference added, parts of Section 5 and the Appendix
removed, the omitted material can be found in an extended form in
arXiv:1808.0515
Status of background-independent coarse-graining in tensor models for quantum gravity
A background-independent route towards a universal continuum limit in
discrete models of quantum gravity proceeds through a background-independent
form of coarse graining. This review provides a pedagogical introduction to the
conceptual ideas underlying the use of the number of degrees of freedom as a
scale for a Renormalization Group flow. We focus on tensor models, for which we
explain how the tensor size serves as the scale for a background-independent
coarse-graining flow. This flow provides a new probe of a universal continuum
limit in tensor models. We review the development and setup of this tool and
summarize results in the 2- and 3-dimensional case. Moreover, we provide a
step-by-step guide to the practical implementation of these ideas and tools by
deriving the flow of couplings in a rank-4-tensor model. We discuss the
phenomenon of dimensional reduction in these models and find tentative first
hints for an interacting fixed point with potential relevance for the continuum
limit in four-dimensional quantum gravity.Comment: 28 pages, Review prepared for the special issue "Progress in Group
Field Theory and Related Quantum Gravity Formalisms" in "Universe
Fivebrane Instanton Corrections to the Universal Hypermultiplet
We analyze the Neveu-Schwarz fivebrane instanton in type IIA string theory
compactifications on rigid Calabi-Yau threefolds, in the low-energy
supergravity approximation. It there appears as a finite action solution to the
Euclidean equations of motion of a double-tensor multiplet (dual to the
universal hypermultiplet) coupled to N=2, D=4 supergravity. We determine the
bosonic and fermionic zero modes, and the single-centered instanton measure on
the moduli space of collective coordinates. The results are then used to
compute, in the semiclassical approximation, correlation functions that
nonperturbatively correct the universal hypermultiplet moduli space geometry of
the low-energy effective action. We find that only the Ramond-Ramond sector
receives corrections, and we discuss the breaking of isometries due to
instantons.Comment: 48 pages, v2: improved version with some correction
- …