162 research outputs found
Improved Complexity Analysis of the Sinkhorn and Greenkhorn Algorithms for Optimal Transport
The Sinkhorn algorithm is a widely used method for solving the optimal
transport problem, and the Greenkhorn algorithm is one of its variants. While
there are modified versions of these two algorithms whose computational
complexities are to achieve an
-accuracy, the best known complexities for the vanilla versions
are . In this paper we fill this
gap and show that the complexities of the vanilla Sinkhorn and Greenkhorn
algorithms are indeed . The
analysis relies on the equicontinuity of the dual variables of the entropic
regularized optimal transport problem, which is of independent interest
Phononic real Chern insulator with protected corner modes in graphynes
Higher-order topological insulators have attracted great research interest
recently. Different from conventional topological insulators, higher-order
topological insulators do not necessarily require spin-orbit coupling, which
makes it possible to realize them in spinless systems. Here, we study phonons
in 2D graphyne family materials. By using first-principle calculations and
topology/symmetry analysis, we find that phonons in both graphdiyne and
-graphyne exhibit a second-order topology, which belongs to the
specific case known as real Chern insulator. We identify the nontrivial
phononic band gaps, which are characterized by nontrivial real Chern numbers
enabled by the spacetime inversion symmetry. The protected phonon corner modes
are verified by the calculation on a finite-size nanodisk. Our study extends
the scope of higher-order topology to phonons in real materials. The spatially
localized phonon modes could be useful for novel phononic applications.Comment: 6 pages, 5figure
Berry connection polarizability tensor and third-order Hall effect
One big achievement in modern condensed matter physics is the recognition of
the importance of various band geometric quantities in physical effects. As
prominent examples, Berry curvature and Berry curvature dipole are connected to
the linear and the second-order Hall effects, respectively. Here, we show that
the Berry connection polarizability (BCP) tensor, as another intrinsic band
geometric quantity, plays a key role in the third-order Hall effect. Based on
the extended semiclassical formalism, we develop a theory for the third-order
charge transport and derive explicit formulas for the third-order conductivity.
Our theory is applied to the two-dimensional (2D) Dirac model to investigate
the essential features of BCP and the third-order Hall response. We further
demonstrate the combination of our theory with the first-principles
calculations to study a concrete material system, the monolayer FeSe. Our work
establishes a foundation for the study of third-order transport effects, and
reveals the third-order Hall effect as a tool for characterizing a large class
of materials and for probing the BCP in band structure.Comment: 7 pages, 4 figure
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