40,036 research outputs found
Order-from-quantum disorder effects and Zeeman field tuned quantum phase transitions in a bosonic quantum anomalous Hall system
We study possible many body phenomena in the recent experimentally realized
weakly interacting quantum anomalous Hall system of spinor bosons by Wu, et.al,
Science 354, 83-88 (2016). At a zero Zeeman field , by incorporating order
from quantum disorder effects, we determine the quantum ground state to be a XY-antiferromagnetic superfluid state and also evaluate its excitation
spectra. At a finite small , the competition between the Zeeman energy and
the effective potential generated by the order from the quantum disorder leads
to a canted antiferromagnetic superfluid state, then drives a second order
transition to a spin-polarized superfluid state along the direction. The
transition is in the same universality class as the zero density superfluid to
Mott transition. Scaling behaviours of various physical quantities are derived.
The ongoing experimental efforts to detect these novel phenomena are discussed.Comment: 5 pages main text + 4 pages supplementary material
Worst-case Complexity of Cyclic Coordinate Descent: Gap with Randomized Version
This paper concerns the worst-case complexity of cyclic coordinate descent
(C-CD) for minimizing a convex quadratic function, which is equivalent to
Gauss-Seidel method and can be transformed to Kaczmarz method and projection
onto convex sets (POCS). We observe that the known provable complexity of C-CD
can be times slower than randomized coordinate descent (R-CD), but no
example was rigorously proven to exhibit such a large gap. In this paper we
show that the gap indeed exists. We prove that there exists an example for
which C-CD takes at least
operations, where is related to Demmel's condition number
and it determines the convergence rate of R-CD. It implies that in the worst
case C-CD can indeed be times slower than R-CD, which has complexity
. Note that for this
example, the gap exists for any fixed update order, not just a particular
order. Based on the example, we establish several almost tight complexity
bounds of C-CD for quadratic problems. One difficulty with the analysis is that
the spectral radius of a non-symmetric iteration matrix does not necessarily
constitute a \textit{lower bound} for the convergence rate.
An immediate consequence is that for Gauss-Seidel method, Kaczmarz method and
POCS, there is also an gap between the cyclic versions and randomized
versions (for solving linear systems). We also show that the classical
convergence rate of POCS by Smith, Solmon and Wager [1] is always worse and
sometimes can be infinitely times worse than our bound.Comment: 47 pages. Add a few tables to summarize the main convergence rates;
add comparison with classical POCS bound; add discussions on another exampl
Rigidity of Graph Joins and Hendrickson's Conjecture
Whiteley \cite{wh} gives a complete characterization of the infinitesimal
flexes of complete bipartite frameworks. Our work generalizes a specific
infinitesimal flex to include joined graphs, a family of graphs that contain
the complete bipartite graphs. We use this characterization to identify new
families of counterexamples, including infinite families, in and above
to Hendrickson's conjecture on generic global rigidity
Quantum spin liquids in a square lattice subject to an Abelian flux
We report that a possible Z2 quantum spin liquid (QSL) can be observed in a
new class of frustrated system: spinor bosons subject to a pi flux in a square
lattice. We construct a new class of Ginsburg-Landau (GL) type of effective
action to classify possible quantum or topological phases at any coupling
strengths. It can be used to reproduce the frustrated SF with the 4 sublattice
coplanar spin structure plus its excitations in the weak
coupling limit and the FM Mott plus its excitations in the strong coupling
limit achieved in our previous work. It also establishes deep and intrinsic
connections between the GL effective action and the order from quantum disorder
(OFQD) phenomena in the weak coupling limit. Most importantly, it predicts two
possible new phases at intermediate couplings: a FM SF phase or a frustrated
magnetic Mott phase. We argue that the latter one is more likely and melts into
a quantum spin liquid (QSL) phase. If the heating issue can be under a
reasonable control at intermediate couplings , the topological
order of the QSL maybe uniquely probed by the current cold atom or
photonic experimental techniques.Comment: 13 pages, 3 figure
Periodic Table of SYK and supersymmetric SYK
We develop a systematic and unified random matrix theory to classify
Sachdev-Ye-Kitaev (SYK) and supersymmetric (SUSY) SYK models and also work out
the structure of the energy levels in one periodic table. The SYK with even
- and SUSY SYK with odd -body interaction, even or odd number of
Majorana fermions are put on the same footing in the minimal Hilbert space,
and double Bott periodicity are identified. Exact
diagonalizations are performed to study both the bulk energy level statistics
and hard edge behaviours. A new moment ratio of the smallest positive
eigenvalue is introduced to determine hard edge index efficiently. Excellent
agreements between the ED results and the symmetry classifications are
demonstrated. Our complete and systematic methods can be transformed to map out
more complicated periodic tables of SYK models with more degree of freedoms,
tensor models and symmetry protected topological phases. Possible
classification of charge neutral quantum black holes are hinted.Comment: One Table, 3 Figures, 22 page
Improved Algorithms for Exact and Approximate Boolean Matrix Decomposition
An arbitrary Boolean matrix can be decomposed {\em exactly}
as , where (resp. ) is an (resp. )
Boolean matrix and denotes the Boolean matrix multiplication operator.
We first prove an exact formula for the Boolean matrix such that holds, where is maximal in the sense that if any 0 element in is
changed to a 1 then this equality no longer holds. Since minimizing is
NP-hard, we propose two heuristic algorithms for finding suboptimal but good
decomposition. We measure the performance (in minimizing ) of our algorithms
on several real datasets in comparison with other representative heuristic
algorithms for Boolean matrix decomposition (BMD). The results on some popular
benchmark datasets demonstrate that one of our proposed algorithms performs as
well or better on most of them. Our algorithms have a number of other
advantages: They are based on exact mathematical formula, which can be
interpreted intuitively. They can be used for approximation as well with
competitive "coverage." Last but not least, they also run very fast. Due to
interpretability issues in data mining, we impose the condition, called the
"column use condition," that the columns of the factor matrix must form a
subset of the columns of .Comment: DSAA201
Weighted stationary phase of higher orders
An th-order first derivative test for oscillatoric integrals is
established. When the phase has a single stationary point, an th-order
asymptotic expansion of a weighted stationary phase integral is proved for
arbitrary . This asymptotic expansion sharpened the classical result
for by Huxley. Possible applications include analysis and analytic number
theory.Comment: arXiv admin note: substantial text overlap with arXiv:1510.0121
Improved subconvexity bounds for GL(2)xGL(3) and GL(3) L-functions by weighted stationary phase
Let be a fixed self-contragradient Hecke-Maass form for , and an even Hecke-Maass form for with Laplace
eigenvalue , . A subconvexity bound
in the eigenvalue aspect is proved for the
central value at of the Rankin-Selberg -function .
Meanwhile, a subconvexity bound in the
aspect is proved for . These bounds improved corresponding
subconvexity bounds proved by Xiaoqing Li (Annals of Mathematics, 2011). The
main technique in the proof, other than those used by Li, is an th-order
asymptotic expansion of a weighted stationary phase integral, for arbitrary
. This asymptotic expansion sharpened the classical result for by
Huxley.Comment: Published in Transactions of the American Mathematical Society online
in December, 201
Towards gauge unified, supersymmetric hidden strong dynamics
We consider a class of models with extra complex scalars that are charged
under both the Standard Model and a hidden strongly coupled gauge
sector, and discuss the scenarios where the new scalars are identified as the
messenger fields that mediate the spontaneously broken supersymmetries from the
hidden sector to the visible sector. The new scalars are embedded into 5-plets
and 10-plets of an gauge group that potentially unifies the Standard
Model gauge groups. The Higgs bosons remain as elementary particles. In the
supersymmetrized version of this class of models, vector-like fermions whose
left-handed components are superperpartners of the new scalars are introduced.
Due to the hidden strong force, the new low-energy scalars hadronize before
decaying and thus evade the common direct searches of the supersymmetric
squarks. This can be seen as a gauge mediation scenario with the scalar
messenger fields forming low-energy bound states. We also discuss the
possibility that among the tower of bound states formed under hidden strong
dynamics (at least the TeV scale) one of them is the dark matter candidate, as
well as the collider signatures (e.g. diphoton, diboson or dijet) of the models
that may show up in the near future.Comment: 33 pages, 6 figures. Expanded the SUSY part. Modified the collider
phenomenology chapte
Ultrafast Manipulation of Valley Pseudospin
The coherent manipulation of spin and pseudospin underlies existing and
emerging quantum technologies, including NMR, quantum communication, and
quantum computation. Valley polarization, associated with the occupancy of
degenerate, but quantum mechanically distinct valleys in momentum space,
closely resembles spin polarization and has been proposed as a pseudospin
carrier for the future quantum electronics. Valley exciton polarization has
been created in the transition metal dichalcogenide (TMDC) monolayers using
excitation by circularly polarized light and has been detected both optically
and electrically. In addition, the existence of coherence in the valley
pseudospin has been identified experimentally. The manipulation of such valley
coherence has, however, remained out of reach. Here we demonstrate an
all-optical control of the valley coherence by means of the pseudomagnetic
field associated with the optical Stark effect. Using below-bandgap circularly
polarized light, we experimentally rotate the valley exciton pseudospin in
monolayer WSe2 on the femtosecond time scale. Both the direction and speed of
the rotation can be optically manipulated by tuning the dynamic phase of
excitons in opposite valleys. This study completes the
generation-manipulation-detection paradigm for valley pseudospin, enabling the
platform of excitons in 2D materials for the control of this novel degree of
freedom in solids.Comment: 9 pages, 4 figure
- …