5,659 research outputs found
Detecting Quantum Critical Points using Bipartite Fluctuations
We show that the concept of bipartite fluctuations F provides a very
efficient tool to detect quantum phase transitions in strongly correlated
systems. Using state of the art numerical techniques complemented with
analytical arguments, we investigate paradigmatic examples for both quantum
spins and bosons. As compared to the von Neumann entanglement entropy, we
observe that F allows to find quantum critical points with a much better
accuracy in one dimension. We further demonstrate that F can be successfully
applied to the detection of quantum criticality in higher dimensions with no
prior knowledge of the universality class of the transition. Promising
approaches to experimentally access fluctuations are discussed for quantum
antiferromagnets and cold gases.Comment: 5 pages, 6 figures + suppl. material; final version, Phys. Rev. Lett.
(in press
General Relation between Entanglement and Fluctuations in One Dimension
In one dimension very general results from conformal field theory and exact
calculations for certain quantum spin systems have established universal
scaling properties of the entanglement entropy between two parts of a critical
system. Using both analytical and numerical methods, we show that if particle
number or spin is conserved, fluctuations in a subsystem obey identical scaling
as a function of subsystem size, suggesting that fluctuations are a useful
quantity for determining the scaling of entanglement, especially in higher
dimensions. We investigate the effects of boundaries and subleading corrections
for critical spin and bosonic chains.Comment: 4 pages, 2 figures. Minor changes, references added
Fluctuations and Entanglement spectrum in quantum Hall states
The measurement of quantum entanglement in many-body systems remains
challenging. One experimentally relevant fact about quantum entanglement is
that in systems whose degrees of freedom map to free fermions with conserved
total particle number, exact relations hold relating the Full Counting
Statistics associated with the bipartite charge fluctuations and the sequence
of R\' enyi entropies. We draw a correspondence between the bipartite charge
fluctuations and the entanglement spectrum, mediated by the R\' enyi entropies.
In the case of the integer quantum Hall effect, we show that it is possible to
reproduce the generic features of the entanglement spectrum from a measurement
of the second charge cumulant only. Additionally, asking whether it is possible
to extend the free fermion result to the fractional quantum Hall
case, we provide numerical evidence that the answer is negative in general. We
further address the problem of quantum Hall edge states described by a
Luttinger liquid, and derive expressions for the spectral functions of the real
space entanglement spectrum at a quantum point contact realized in a quantum
Hall sample.Comment: Final Version. Invited Article, for Special Issue of JSTAT on
"Quantum Entanglement in Condensed Matter Physics
Bipartite Fluctuations as a Probe of Many-Body Entanglement
We investigate in detail the behavior of the bipartite fluctuations of
particle number and spin in many-body quantum systems,
focusing on systems where such U(1) charges are both conserved and fluctuate
within subsystems due to exchange of charges between subsystems. We propose
that the bipartite fluctuations are an effective tool for studying many-body
physics, particularly its entanglement properties, in the same way that noise
and Full Counting Statistics have been used in mesoscopic transport and cold
atomic gases. For systems that can be mapped to a problem of non-interacting
fermions we show that the fluctuations and higher-order cumulants fully encode
the information needed to determine the entanglement entropy as well as the
full entanglement spectrum through the R\'{e}nyi entropies. In this connection
we derive a simple formula that explicitly relates the eigenvalues of the
reduced density matrix to the R\'{e}nyi entropies of integer order for any
finite density matrix. In other systems, particularly in one dimension, the
fluctuations are in many ways similar but not equivalent to the entanglement
entropy. Fluctuations are tractable analytically, computable numerically in
both density matrix renormalization group and quantum Monte Carlo calculations,
and in principle accessible in condensed matter and cold atom experiments. In
the context of quantum point contacts, measurement of the second charge
cumulant showing a logarithmic dependence on time would constitute a strong
indication of many-body entanglement.Comment: 30 pages + 25 pages supplementary materia
The Hanabi Challenge: A New Frontier for AI Research
From the early days of computing, games have been important testbeds for
studying how well machines can do sophisticated decision making. In recent
years, machine learning has made dramatic advances with artificial agents
reaching superhuman performance in challenge domains like Go, Atari, and some
variants of poker. As with their predecessors of chess, checkers, and
backgammon, these game domains have driven research by providing sophisticated
yet well-defined challenges for artificial intelligence practitioners. We
continue this tradition by proposing the game of Hanabi as a new challenge
domain with novel problems that arise from its combination of purely
cooperative gameplay with two to five players and imperfect information. In
particular, we argue that Hanabi elevates reasoning about the beliefs and
intentions of other agents to the foreground. We believe developing novel
techniques for such theory of mind reasoning will not only be crucial for
success in Hanabi, but also in broader collaborative efforts, especially those
with human partners. To facilitate future research, we introduce the
open-source Hanabi Learning Environment, propose an experimental framework for
the research community to evaluate algorithmic advances, and assess the
performance of current state-of-the-art techniques.Comment: 32 pages, 5 figures, In Press (Artificial Intelligence
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