1,155 research outputs found
A cluster algorithm for Lattice Gauge Theories
A new algorithm for simulating compact U(1) lattice gauge theory in three
dimensions is presented which is based on global changes in the configuration
space. We show that this algorithm provides an effective way to extract
partition functions at given external flux. As an application, we study
numerically the finite temperature deconfinement phase transition.Comment: 4 pages, 2 figures. Talk given at the Conference on Computational
Physics, Genova, Italy, Sept. 200
Phase diagram of an extended classical dimer model
We present an extensive numerical study of the critical behavior of dimer
models in three dimensions, focusing on the phase transition between Coulomb
and crystalline columnar phases. The case of attractive interactions between
parallel dimers on a plaquette was shown to undergo a continuous phase
transition with critical exponents close to those of the O(N) tricritical
universality class, a situation which is not easily captured by conventional
field theories. That the dimer model is exactly fine-tuned to a highly
symmetric point is a non trivial statement which needs careful numerical
investigation. In this paper, we perform an extensive Monte Carlo study of a
generalized dimer model with plaquette and cubic interactions and determine its
extended phase diagram. We find that when both interactions favor alignment of
the dimers, the phase transition is first order, in almost all cases. On the
opposite, when interactions compete, the transition becomes continuous, with a
critical exponent \eta ~ 0.2. The existence of a tricritical point between the
two regimes is confirmed by simulations on very large size systems and a
flowgram method. In addition, we find a highly-degenerate crystalline phase at
very low temperature in the frustrated regime which is separated from the
columnar phase by a first order transition.Comment: 12 pages, 13 figure
Valence Bond Entanglement Entropy
We introduce for SU(2) quantum spin systems the Valence Bond Entanglement
Entropy as a counting of valence bond spin singlets shared by two subsystems.
For a large class of antiferromagnetic systems, it can be calculated in all
dimensions with Quantum Monte Carlo simulations in the valence bond basis. We
show numerically that this quantity displays all features of the von Neumann
entanglement entropy for several one-dimensional systems. For two-dimensional
Heisenberg models, we find a strict area law for a Valence Bond Solid state and
multiplicative logarithmic corrections for the Neel phase.Comment: 4 pages, 3 figures, v2: small corrections, published versio
Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
Determining phase diagrams and phase transitions semi-automatically using
machine learning has received a lot of attention recently, with results in good
agreement with more conventional approaches in most cases. When it comes to
more quantitative predictions, such as the identification of universality class
or precise determination of critical points, the task is more challenging. As
an exacting test-bed, we study the Heisenberg spin-1/2 chain in a random
external field that is known to display a transition from a many-body localized
to a thermalizing regime, which nature is not entirely characterized. We
introduce different neural network structures and dataset setups to achieve a
finite-size scaling analysis with the least possible physical bias (no assumed
knowledge on the phase transition and directly inputing wave-function
coefficients), using state-of-the-art input data simulating chains of sizes up
to L=24. In particular, we use domain adversarial techniques to ensure that the
network learns scale-invariant features. We find a variability of the output
results with respect to network and training parameters, resulting in
relatively large uncertainties on final estimates of critical point and
correlation length exponent which tend to be larger than the values obtained
from conventional approaches. We put the emphasis on interpretability
throughout the paper and discuss what the network appears to learn for the
various used architectures. Our findings show that a it quantitative analysis
of phase transitions of unknown nature remains a difficult task with neural
networks when using the minimally engineered physical input.Comment: v2: published versio
Linear vector optimization and European option pricing under proportional transaction costs
A method for pricing and superhedging European options under proportional
transaction costs based on linear vector optimisation and geometric duality
developed by Lohne & Rudloff (2014) is compared to a special case of the
algorithms for American type derivatives due to Roux & Zastawniak (2014). An
equivalence between these two approaches is established by means of a general
result linking the support function of the upper image of a linear vector
optimisation problem with the lower image of the dual linear optimisation
problem
Many-body localization: an introduction and selected topics
What happens in an isolated quantum system when both disorder and
interactions are present? Over the recent years, the picture of a
non-thermalizing phase of matter, the many-localized phase, has emerged as a
stable solution. We present a basic introduction to the topic of many-body
localization, using the simple example of a quantum spin chain which allows us
to illustrate several of the properties of this phase. We then briefly review
the current experimental research efforts probing this physics. The largest
part of this review is a selection of more specialized questions, some of which
are currently under active investigation. We conclude by summarizing the
connections between many-body localization and quantum simulations.Comment: Review article. 28 pages, 8 figures, Comptes Rendus Physique (2018
Out-of-time-ordered measurements as a probe of quantum dynamics
Probing the out-of-equilibrium dynamics of quantum matter has gained renewed
interest owing to immense experimental progress in artifcial quantum systems.
Dynamical quantum measures such as the growth of entanglement entropy (EE) and
out-of-time ordered correlators (OTOCs) have been shown, theoretically, to
provide great insight by exposing subtle quantum features invisible to
traditional measures such as mass transport. However, measuring them in
experiments requires either identical copies of the system, an ancilla qubit
coupled to the whole system, or many measurements on a single copy, thereby
making scalability extremely complex and hence, severely limiting their
potential. Here, we introduce an alternate quantity the out-of-time-ordered
measurement (OTOM) which involves measuring a single observable on a single
copy of the system, while retaining the distinctive features of the OTOCs. We
show, theoretically, that OTOMs are closely related to OTOCs in a doubled
system with the same quantum statistical properties as the original system.
Using exact diagonalization, we numerically simulate classical mass transport,
as well as quantum dynamics through computations of the OTOC, the OTOM, and the
EE in quantum spin chain models in various interesting regimes (including
chaotic and many-body localized systems). Our results demonstrate that an OTOM
can successfully reveal subtle aspects of quantum dynamics hidden to classical
measures, and crucially, provide experimental access to them.Comment: 7 pages, 4 figure
The semiflexible fully-packed loop model and interacting rhombus tilings
Motivated by a recent adsorption experiment [M.O. Blunt et al., Science 322,
1077 (2008)], we study tilings of the plane with three different types of
rhombi. An interaction disfavors pairs of adjacent rhombi of the same type.
This is shown to be a special case of a model of fully-packed loops with
interactions between monomers at distance two along a loop. We solve the latter
model using Coulomb gas techniques and show that its critical exponents vary
continuously with the interaction strenght. At low temperature it undergoes a
Kosterlitz-Thouless transition to an ordered phase, which is predicted from
numerics to occur at a temperature T \sim 110K in the experiments.Comment: 4 pages, 4 figures, v2: corrected typo, v3: minor modifications,
published versio
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