3,175 research outputs found
Entanglement Structure of Deconfined Quantum Critical Points
We study the entanglement properties of deconfined quantum critical points.
We show not only that these critical points may be distinguished by their
entanglement structure but also that they are in general more highly entangled
that conventional critical points. We primarily focus on computations of the
entanglement entropy of deconfined critical points in 2+1 dimensions, drawing
connections to topological entanglement entropy and a recent conjecture on the
monotonicity under RG flow of universal terms in the entanglement entropy. We
also consider in some detail a variety of issues surrounding the extraction of
universal terms in the entanglement entropy. Finally, we compare some of our
results to recent numerical simulations.Comment: 12 pages, 4 figure
Entanglement, Replicas, and Thetas
We compute the single-interval Renyi entropy (replica partition function) for
free fermions in 1+1d at finite temperature and finite spatial size by two
methods: (i) using the higher-genus partition function on the replica Riemann
surface, and (ii) using twist operators on the torus. We compare the two
answers for a restricted set of spin structures, leading to a non-trivial
proposed equivalence between higher-genus Siegel -functions and Jacobi
-functions. We exhibit this proposal and provide substantial evidence
for it. The resulting expressions can be elegantly written in terms of Jacobi
forms. Thereafter we argue that the correct Renyi entropy for modular-invariant
free-fermion theories, such as the Ising model and the Dirac CFT, is given by
the higher-genus computation summed over all spin structures. The result
satisfies the physical checks of modular covariance, the thermal entropy
relation, and Bose-Fermi equivalence.Comment: 34 page
Entropy and quantum gravity
We give a review, in the style of an essay, of the author's 1998
matter-gravity entanglement hypothesis which, unlike the standard approach to
entropy based on coarse-graining, offers a definition for the entropy of a
closed system as a real and objective quantity. We explain how this approach
offers an explanation for the Second Law of Thermodynamics in general and a
non-paradoxical understanding of information loss during black hole formation
and evaporation in particular. It also involves a radically different from
usual description of black hole equilibrium states in which the total state of
a black hole in a box together with its atmosphere is a pure state -- entangled
in just such a way that the reduced state of the black hole and of its
atmosphere are each separately approximately thermal. We also briefly recall
some recent work of the author which involves a reworking of the string-theory
understanding of black hole entropy consistent with this alternative
description of black hole equilibrium states and point out that this is free
from some unsatisfactory features of the usual string theory understanding. We
also recall the author's recent arguments based on this alternative description
which suggest that the AdS/CFT correspondence is a bijection between the
boundary CFT and just the matter degrees of freedom of the bulk theory.Comment: 15 pages. Considerably enlarged. 3 figures and many references added.
Also published in the recent special issue "Entropy in Quantum Gravity and
Quantum Cosmology" (ed. Remo Garattini) of the online journal "Entropy".
(Note: that journal version will soon be replaced with an updated version
where some typesetting errors are corrected. This arXiv version is also free
from those errors.
Brick Walls and AdS/CFT
We discuss the relationship between the bulk-boundary correspondence in
Rehren's algebraic holography (and in other 'fixed-background' approaches to
holography) and in mainstream 'Maldacena AdS/CFT'. Especially, we contrast the
understanding of black-hole entropy from the viewpoint of QFT in curved
spacetime -- in the framework of 't Hooft's 'brick wall' model -- with the
understanding based on Maldacena AdS/CFT. We show that the brick-wall
modification of a Klein Gordon field in the Hartle-Hawking-Israel state on
1+2-Schwarzschild AdS (BTZ) has a well-defined boundary limit with the same
temperature and entropy as the brick-wall-modified bulk theory. One of our main
purposes is to point out a close connection, for general AdS/CFT situations,
between the puzzle raised by Arnsdorf and Smolin regarding the relationship
between Rehren's algebraic holography and mainstream AdS/CFT and the puzzle
embodied in the 'correspondence principle' proposed by Mukohyama and Israel in
their work on the brick-wall approach to black hole entropy. Working on the
assumption that similar results will hold for bulk QFT other than the Klein
Gordon field and for Schwarzschild AdS in other dimensions, and recalling the
first author's proposed resolution to the Mukohyama-Israel puzzle based on his
'matter-gravity entanglement hypothesis', we argue that, in Maldacena AdS/CFT,
the algebra of the boundary CFT is isomorphic only to a proper subalgebra of
the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of
bulk and boundary theories are still the 'same' -- the total bulk state being
pure, while the boundary state is mixed (thermal). We also argue from the
finiteness of its boundary (and hence, on our assumptions, also bulk) entropy
at finite temperature, that the Rehren dual of the Maldacena boundary CFT
cannot itself be a QFT and must, instead, presumably be something like a string
theory.Comment: 54 pages, 3 figures. Arguments strengthened in the light of B.S. Kay
`Instability of Enclosed Horizons' arXiv:1310.739
Black Hole Macro-Quantumness
It is a common wisdom that properties of macroscopic bodies are well
described by (semi)classical physics. As we have suggested this wisdom is not
applicable to black holes. Despite being macroscopic, black holes are quantum
objects. They represent Bose-Einstein condensates of N-soft gravitons at the
quantum critical point, where N Bogoliubov modes become gapless. As a result,
physics governing arbitrarily-large black holes (e.g., of galactic size) is a
quantum physics of the collective Bogoiliubov modes. This fact introduces a new
intrinsically-quantum corrections in form of 1/N, as opposed to exp(-N). These
corrections are unaccounted by the usual semiclassical expansion in h and
cannot be recast in form of a quantum back-reaction to classical metric.
Instead the metric itself becomes an approximate entity. These 1/N corrections
abolish the presumed properties of black holes, such as non existence of hair,
and are the key to nullifying the so-called information paradox.Comment: 14 page
Parts of Quantum States
It is shown that generic N-party pure quantum states (with equidimensional
subsystems) are uniquely determined by their reduced states of just over half
the parties; in other words, all the information in almost all N-party pure
states is in the set of reduced states of just over half the parties. For N
even, the reduced states in fewer than N/2 parties are shown to be an
insufficient description of almost all states (similar results hold when N is
odd). It is noted that Real Algebraic Geometry is a natural framework for any
analysis of parts of quantum states: two simple polynomials, a quadratic and a
cubic, contain all of their structure. Algorithmic techniques are described
which can provide conditions for sets of reduced states to belong to pure or
mixed states.Comment: 10 pages, 1 figur
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