2,927 research outputs found
Hidden quasi one-dimensional superconductivity in SrRuO
Using an asymptotically exact weak coupling analysis of a multi-orbital
Hubbard model of the electronic structure of \SRO, we show that the interplay
between spin and charge fluctuations leads unequivocally to triplet pairing
which originates in the quasi-one dimensional bands. The resulting
superconducting state spontaneously breaks time-reversal symmetry and is of the
form with sharp gap minima and a d-vector
that is only {\it weakly} pinned. The supercondutor is topologically {\it
trivial} and hence lacks robust chiral Majorana fermion modes along the
boundary. The absence of topologically protected edge modes could explain the
surprising absence of experimentally detectable edge currents in this system.Comment: 5 pages, 3 figure
Guaranteed Rank Minimization via Singular Value Projection
Minimizing the rank of a matrix subject to affine constraints is a
fundamental problem with many important applications in machine learning and
statistics. In this paper we propose a simple and fast algorithm SVP (Singular
Value Projection) for rank minimization with affine constraints (ARMP) and show
that SVP recovers the minimum rank solution for affine constraints that satisfy
the "restricted isometry property" and show robustness of our method to noise.
Our results improve upon a recent breakthrough by Recht, Fazel and Parillo
(RFP07) and Lee and Bresler (LB09) in three significant ways:
1) our method (SVP) is significantly simpler to analyze and easier to
implement,
2) we give recovery guarantees under strictly weaker isometry assumptions
3) we give geometric convergence guarantees for SVP even in presense of noise
and, as demonstrated empirically, SVP is significantly faster on real-world and
synthetic problems.
In addition, we address the practically important problem of low-rank matrix
completion (MCP), which can be seen as a special case of ARMP. We empirically
demonstrate that our algorithm recovers low-rank incoherent matrices from an
almost optimal number of uniformly sampled entries. We make partial progress
towards proving exact recovery and provide some intuition for the strong
performance of SVP applied to matrix completion by showing a more restricted
isometry property. Our algorithm outperforms existing methods, such as those of
\cite{RFP07,CR08,CT09,CCS08,KOM09,LB09}, for ARMP and the matrix-completion
problem by an order of magnitude and is also significantly more robust to
noise.Comment: An earlier version of this paper was submitted to NIPS-2009 on June
5, 200
Particle-hole condensates of higher angular momentum in hexagonal systems
Hexagonal lattice systems (e.g. triangular, honeycomb, kagome) possess a
multidimensional irreducible representation corresponding to and
symmetry. Consequently, various unconventional phases that combine
these -wave representations can occur, and in so doing may break
time-reversal and spin rotation symmetries. We show that hexagonal lattice
systems with extended repulsive interactions can exhibit instabilities in the
particle-hole channel to phases with either or
symmetry. When lattice translational symmetry is preserved, the phase
corresponds to nematic order in the spin-channel with broken time-reversal
symmetry, known as the phase. On the other hand, lattice translation
symmetry can be broken, resulting in various density wave
orders. In the weak-coupling limit, when the Fermi surface lies close to a van
Hove singularity, instabilities of both types are obtained in a controlled
fashion.Comment: 6 pages, 3 figures. Journal reference adde
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