Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Properties of Modular Hamiltonians on Entanglement Plateaux   The modular Hamiltonian of reduced states, given essentially by the logarithm
of the reduced density matrix, plays an important role within the AdS/CFT
correspondence in view of its relation to quantum information. In particular,
it is an essential ingredient for quantum information measures of distances
between states, such as the relative entropy and the Fisher information metric.
However, the modular Hamiltonian is known explicitly only for a few examples.
For a family of states $\rho_\lambda$ that is parametrized by a scalar
$\lambda$, the first order contribution in $\tilde\lambda=\lambda-\lambda_0$ of
the modular Hamiltonian to the relative entropy between $\rho_\lambda$ and a
reference state $\rho_{\lambda_0}$ is completely determined by the entanglement
entropy, via the first law of entanglement. For several examples, e.g. for
ball-shaped regions in the ground state of CFTs, higher order contributions are
known to vanish. In these cases the modular Hamiltonian contributes to the
Fisher information metric in a trivial way. We investigate under which
conditions the modular Hamiltonian provides a non-trivial contribution to the
Fisher information metric, i.e. when the contribution of the modular
Hamiltonian to the relative entropy is of higher order in $\tilde{\lambda}$. We
consider one-parameter families of reduced states on two entangling regions
that form an entanglement plateau, i.e. the entanglement entropies of the two
regions saturate the Araki-Lieb inequality. We show that in general, at least
one of the relative entropies of the two entangling regions is expected to
involve $\tilde{\lambda}$ contributions of higher order from the modular
Hamiltonian. Furthermore, we consider the implications of this observation for
prominent AdS/CFT examples that form entanglement plateaux in the large $N$
limit.

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The categories of this paper are: math
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org