253 research outputs found
Entanglement spectrum and boundary theories with projected entangled-pair states
In many physical scenarios, close relations between the bulk properties of
quantum systems and theories associated to their boundaries have been observed.
In this work, we provide an exact duality mapping between the bulk of a quantum
spin system and its boundary using Projected Entangled Pair States (PEPS). This
duality associates to every region a Hamiltonian on its boundary, in such a way
that the entanglement spectrum of the bulk corresponds to the excitation
spectrum of the boundary Hamiltonian. We study various specific models, like a
deformed AKLT [1], an Ising-type [2], and Kitaev's toric code [3], both in
finite ladders and infinite square lattices. In the latter case, some of those
models display quantum phase transitions. We find that a gapped bulk phase with
local order corresponds to a boundary Hamiltonian with local interactions,
whereas critical behavior in the bulk is reflected on a diverging interaction
length of the boundary Hamiltonian. Furthermore, topologically ordered states
yield non-local Hamiltonians. As our duality also associates a boundary
operator to any operator in the bulk, it in fact provides a full holographic
framework for the study of quantum many-body systems via their boundary.Comment: 13 pages, 14 figure
Thermodynamics and area in Minkowski space: Heat capacity of entanglement
Tracing over the degrees of freedom inside (or outside) a sub-volume V of
Minkowski space in a given quantum state |psi>, results in a statistical
ensemble described by a density matrix rho. This enables one to relate quantum
fluctuations in V when in the state |psi>, to statistical fluctuations in the
ensemble described by rho. These fluctuations scale linearly with the surface
area of V. If V is half of space, then rho is the density matrix of a canonical
ensemble in Rindler space. This enables us to `derive' area scaling of
thermodynamic quantities in Rindler space from area scaling of quantum
fluctuations in half of Minkowski space. When considering shapes other than
half of Minkowski space, even though area scaling persists, rho does not have
an interpretation as a density matrix of a canonical ensemble in a curved, or
geometrically non-trivial, background.Comment: 17 page
Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
We compute the entropy of entanglement between the first spins and the
rest of the system in the ground states of a general class of quantum
spin-chains. We show that under certain conditions the entropy can be expressed
in terms of averages over ensembles of random matrices. These averages can be
evaluated, allowing us to prove that at critical points the entropy grows like
as , where and are determined explicitly. In an important class of systems,
is equal to one-third of the central charge of an associated Virasoro algebra.
Our expression for therefore provides an explicit formula for the
central charge.Comment: 4 page
Effective Gravitational Field of Black Holes
The problem of interpretation of the \hbar^0-order part of radiative
corrections to the effective gravitational field is considered. It is shown
that variations of the Feynman parameter in gauge conditions fixing the general
covariance are equivalent to spacetime diffeomorphisms. This result is proved
for arbitrary gauge conditions at the one-loop order. It implies that the
gravitational radiative corrections of the order \hbar^0 to the spacetime
metric can be physically interpreted in a purely classical manner. As an
example, the effective gravitational field of a black hole is calculated in the
first post-Newtonian approximation, and the secular precession of a test
particle orbit in this field is determined.Comment: 8 pages, LaTeX, 1 eps figure. Proof of the theorem and typos
correcte
Universality of Entropy Scaling in 1D Gap-less Models
We consider critical models in one dimension. We study the ground state in
thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu,
and Schumacher, we use the entropy of a sub-system as a measure of
entanglement. We calculate the entropy of a part of the ground state. At zero
temperature it describes entanglement of this part with the rest of the ground
state. We obtain an explicit formula for the entropy of the subsystem at low
temperature. At zero temperature we reproduce a logarithmic formula of Holzhey,
Larsen and Wilczek. Our derivation is based on the second law of
thermodynamics. The entropy of a subsystem is calculated explicitly for Bose
gas with delta interaction, the Hubbard model and spin chains with arbitrary
value of spin.Comment: A section on spin chains with arbitrary value of spin is included.
The entropy of a subsystem is calculated explicitly as a function of spin.
References update
Emission rates, the Correspondence Principle and the Information Paradox
When we vary the moduli of a compactification it may become entropically
favourable at some point for a state of branes and strings to rearrange itself
into a new configuration. We observe that for the elementary string with two
large charges such a rearrangement happens at the `correspondence point' where
the string becomes a black hole. For smaller couplings it is entropically
favourable for the excitations to be vibrations of the string, while for larger
couplings the favoured excitations are pairs of solitonic 5-branes attached to
the string; this helps resolve some recently noted difficulties with matching
emission properties of the string to emission properties of the black hole. We
also examine the change of state when a black hole is placed in a spacetime
with an additional compact direction, and the size of this direction is varied.
These studies suggest a mechanism that might help resolve the information
paradox.Comment: harvmac, 28 page
Dilaton Black Holes with Electric Charge
Static spherically symmetric solutions of the Einstein-Maxwell gravity with
the dilaton field are described. The solutions correspond to black holes and
are generalizations of the previously known dilaton black hole solution. In
addition to mass and electric charge these solutions are labeled by a new
parameter, the dilaton charge of the black hole. Different effects of the
dilaton charge on the geometry of space-time of such black holes are studied.
It is shown that in most cases the scalar curvature is divergent at the
horizons. Another feature of the dilaton black hole is that there is a finite
interval of values of electric charge for which no black hole can exist.Comment: 20 pages, LaTeX file + 1 figure, CALT-68-1885. (the postscript file
is improved
Entropy for dilatonic black hole
The area formula for entropy is extended to the case of a dilatonic black
hole. The entropy of a scalar field in the background of such a black hole is
calculated semiclassically. The area and cutoff dependences are normal {\it
except in the extremal case}, where the area is zero but the entropy nonzero.Comment: 13 pages (Applicability of area formula justified and a reference
added
Entropy, holography and the second law
The geometric entropy in quantum field theory is not a Lorentz scalar and has
no invariant meaning, while the black hole entropy is invariant.
Renormalization of entropy and energy for reduced density matrices may lead to
the negative free energy even if no boundary conditions are imposed. Presence
of particles outside the horizon of a uniformly accelerated observer prevents
the description in terms of a single Unruh temperature.Comment: 4 pages, RevTex 4, 1 eps figur
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