157 research outputs found
Geodesic-Einstein metrics and nonlinear stabilities
In this paper, we introduce notions of nonlinear stabilities for a relative
ample line bundle over a holomorphic fibration and define the notion of a
geodesic-Einstein metric on this line bundle, which generalize the classical
stabilities and Hermitian-Einstein metrics of holomorphic vector bundles. We
introduce a Donaldson type functional and show that this functional attains its
absolute minimum at geodesic-Einstein metrics, and we also discuss the
relations between the existence of geodesic-Einstein metrics and the nonlinear
stabilities of the line bundle. As an application, we will prove that a
holomorphic vector bundle admits a Finsler-Einstein metric if and only if it
admits a Hermitian-Einstein metric, which answers a problem posed by S.
Kobayashi.Comment: 21 pages, the final version, to appear in Transactions of the
American Mathematical Societ
Self-Learning Monte Carlo Method: Continuous-Time Algorithm
The recently-introduced self-learning Monte Carlo method is a general-purpose
numerical method that speeds up Monte Carlo simulations by training an
effective model to propose uncorrelated configurations in the Markov chain. We
implement this method in the framework of continuous time Monte Carlo method
with auxiliary field in quantum impurity models. We introduce and train a
diagram generating function (DGF) to model the probability distribution of
auxiliary field configurations in continuous imaginary time, at all orders of
diagrammatic expansion. By using DGF to propose global moves in configuration
space, we show that the self-learning continuous-time Monte Carlo method can
significantly reduce the computational complexity of the simulation.Comment: 6 pages, 5 figures + 2 page supplemental materials, to be published
in Phys. Rev. B Rapid communication sectio
Self-Learning Monte Carlo Method in Fermion Systems
We develop the self-learning Monte Carlo (SLMC) method, a general-purpose
numerical method recently introduced to simulate many-body systems, for
studying interacting fermion systems. Our method uses a highly-efficient update
algorithm, which we design and dub "cumulative update", to generate new
candidate configurations in the Markov chain based on a self-learned bosonic
effective model. From general analysis and numerical study of the double
exchange model as an example, we find the SLMC with cumulative update
drastically reduces the computational cost of the simulation, while remaining
statistically exact. Remarkably, its computational complexity is far less than
the conventional algorithm with local updates
Self-learning Monte Carlo with Deep Neural Networks
Self-learning Monte Carlo (SLMC) method is a general algorithm to speedup MC
simulations. Its efficiency has been demonstrated in various systems by
introducing an effective model to propose global moves in the configuration
space. In this paper, we show that deep neural networks can be naturally
incorporated into SLMC, and without any prior knowledge, can learn the original
model accurately and efficiently. Demonstrated in quantum impurity models, we
reduce the complexity for a local update from in
Hirsch-Fye algorithm to , which is a
significant speedup especially for systems at low temperatures.Comment: 6 pages, 4 figures + 4 pages of supplemental materia
In-Plane Ferroelectric Tunnel Junction
The ferroelectric material is an important platform to realize non-volatile
memories. So far, existing ferroelectric memory devices utilize out-of-plane
polarization in ferroelectric thin films. In this paper, we propose a new type
of random-access memory (RAM) based on ferroelectric thin films with the
in-plane polarization called "in-plane ferroelectric tunnel junction". Apart
from non-volatility, lower power usage and faster writing operation compared
with traditional dynamic RAMs, our proposal has the advantage of faster reading
operation and non-destructive reading process, thus overcomes the
write-after-read problem that widely exists in current ferroelectric RAMs. The
recent discovered room-temperature ferroelectric IV-VI semiconductor thin films
is a promising material platform to realize our proposal.Comment: 6 pages, 3 figures + 3 pages of supplemental materia
- …