328,441 research outputs found
Tuning Kinetic Magnetism of Strongly Correlated Electrons via Staggered Flux
We explore the kinetic magnetism of the infinite- repulsive Hubbard models
at low hole densities on various lattices with nearest-neighbor hopping
integrals modulated by a staggered magnetic flux . Tuning from
0 to makes the ground state (GS) change from a Nagaoka-type ferromagnetic
state to a Haerter-Shastry-type antiferromagnetic state at a critical ,
with both states being of kinetic origin. Intra-plaquette spin correlation, as
well as the GS energy, signals such a quantum criticality. This tunable kinetic
magnetism is generic, and appears in chains, ladders and two-dimensional
lattices with squares or triangles as elementary constituents.Comment: 4 pages, 5 figures, 1 tabl
A new approach to the study of the ground-state properties of 2D Ising spin glass
A new approach known as flat histogram method is used to study the +/-J Ising
spin glass in two dimensions. Temperature dependence of the energy, the
entropy, and other physical quantities can be easily calculated and we give the
results for the zero-temperature limit. For the ground-state energy and entropy
of an infinite system size, we estimate e0 = -1.4007 +/- 0.0085 and s0 = 0.0709
+/- 0.006, respectively. Both of them agree well with previous calculations.
The time to find the ground-states as well as the tunneling times of the
algorithm are also reported and compared with other methods.Comment: 11 pages, 4 figure
Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters
Bayesian optimisation has gained great popularity as a tool for optimising
the parameters of machine learning algorithms and models. Somewhat ironically,
setting up the hyper-parameters of Bayesian optimisation methods is notoriously
hard. While reasonable practical solutions have been advanced, they can often
fail to find the best optima. Surprisingly, there is little theoretical
analysis of this crucial problem in the literature. To address this, we derive
a cumulative regret bound for Bayesian optimisation with Gaussian processes and
unknown kernel hyper-parameters in the stochastic setting. The bound, which
applies to the expected improvement acquisition function and sub-Gaussian
observation noise, provides us with guidelines on how to design hyper-parameter
estimation methods. A simple simulation demonstrates the importance of
following these guidelines.Comment: 16 pages, 1 figur
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