8,353 research outputs found
Planar Para Algebras, Reflection Positivity
We define a planar para algebra, which arises naturally from combining planar
algebras with the idea of para symmetry in physics. A
subfactor planar para algebra is a Hilbert space representation of planar
tangles with parafermionic defects, that are invariant under para isotopy. For
each , we construct a family of subfactor planar para algebras
which play the role of Temperley-Lieb-Jones planar algebras. The first example
in this family is the parafermion planar para algebra (PAPPA). Based on this
example, we introduce parafermion Pauli matrices, quaternion relations, and
braided relations for parafermion algebras which one can use in the study of
quantum information. An important ingredient in planar para algebra theory is
the string Fourier transform (SFT), that we use on the matrix algebra generated
by the Pauli matrices. Two different reflections play an important role in the
theory of planar para algebras. One is the adjoint operator; the other is the
modular conjugation in Tomita-Takesaki theory. We use the latter one to define
the double algebra and to introduce reflection positivity. We give a new and
geometric proof of reflection positivity, by relating the two reflections
through the string Fourier transform.Comment: 41 page
A Mathematical Picture Language Program
We give an overview of our philosophy of pictures in mathematics. We
emphasize a bi-directional process between picture language and mathematical
concepts: abstraction and simulation. This motivates a program to understand
different subjects, using virtual and real mathematical concepts simulated by
pictures.Comment: 15 page
Reflection Positivity and Levin-Wen Models
The reflection positivity property has played a central role in both
mathematics and physics, as well as providing a crucial link between the two
subjects. In a previous paper we gave a new geometric approach to understanding
reflection positivity in terms of pictures. Here we give a transparent
algebraic formulation of our pictorial approach. We use insights from this
translation to establish the reflection positivity property for the fashionable
Levin-Wen models with respect both to vacuum and to bulk excitations. We
believe these methods will be useful for understanding a variety of other
problems.Comment: 16 page
Holographic Software for Quantum Networks
We introduce a pictorial approach to quantum information, called holographic
software. Our software captures both algebraic and topological aspects of
quantum networks. It yields a bi-directional dictionary to translate between a
topological approach and an algebraic approach. Using our software, we give a
topological simulation for quantum networks. The string Fourier transform (SFT)
is our basic tool to transform product states into states with maximal
entanglement entropy. We obtain a pictorial interpretation of Fourier
transformation, of measurements, and of local transformations, including the
-qudit Pauli matrices and their representation by Jordan-Wigner
transformations.
We use our software to discover interesting new protocols for multipartite
communication. In summary, we build a bridge linking the theory of planar para
algebras with quantum information.Comment: 48 pages. Accepted for publication in SCIENCE CHINA Mathematic
Qudit Isotopy
We explore a general diagrammatic framework to understand qudits and their
braiding, especially in its relation to entanglement. This involves
understanding the role of isotopy in interpreting diagrams that implement
entangling gates as well as some standard quantum information protocols. We
give qudit Pauli operators and comment on their structure, both from an
algebraic and from a diagrammatic point of view. We explain alternative models
for diagrammatic interpretations of qudits and their transformations. We use
our diagrammatic approach to define an entanglement-relay protocol for
long-distance entanglement. Our approach rests on algebraic and topological
relations discovered in the study of planar para algebras. In summary, this
work provides bridges between the new theory of planar para algebras and
quantum information, especially in questions involving entanglement
Compressed Teleportation
In a previous paper we introduced holographic software for quantum networks,
inspired by work on planar para algebras. This software suggests the definition
of a compressed transformation. Here we utilize the software to find a CT
protocol to teleport compressed transformations. This protocol serves multiple
parties with multiple persons.Comment: 3 page
Long-wavelength deformations and vibrational modes in empty and liquid-filled microtubules and nanotubes: A theoretical study
We propose a continuum model to predict long-wavelength vibrational modes of
empty and liquid-filled tubules that are very hard to reproduce using the
conventional force-constant matrix approach based on atomistic ab initio
calculation. We derive simple quantitative expressions for long-wavelength
longitudinal and torsional acoustic modes, flexural acoustic modes, as well as
the radial breathing mode of empty or liquid-filled tubular structures that are
based on continuum elasticity theory expressions for a thin elastic plate. We
furthermore show that longitudinal and flexural acoustic modes of tubules are
well described by those of an elastic beam resembling a nanowire. Our numerical
results for biological microtubules and carbon nanotubes agree with available
experimental data.Comment: The paper has been accepted by Physical Review
Hidden spin polarization in inversion-symmetric bulk crystals
Spin-orbit coupling (SOC) can induce spin polarization in nonmagnetic 3D
crystals when the inversion symmetry is broken, as manifested by the bulk
Rashba (R-1) and Dresselhaus (D-1) effects. We determine that these spin
polarization effects originate fundamentally from specific atomic site
asymmetries, rather than from the generally accepted asymmetry of the crystal
space-group. This understanding leads to the recognition that a previously
overlooked hidden form of spin polarization should exist in centrosymmetric
materials. Although all energy bands must be doubly degenerate in
centrosymmetric materials, we find that the two components of such doubly
degenerate bands could have opposite polarizations each spatially localized on
one of the two separate sectors forming the inversion partners. We demonstrate
such hidden spin polarizations in centrosymmetric crystals (denoted as R-2 and
D-2) by first-principles calculations. This new understanding could
considerably broaden the range of currently useful spintronic materials and
enable control of spin polarization via operations on atomic scale.Comment: 23 pages, 5 figure
Exponential Family Estimation via Adversarial Dynamics Embedding
We present an efficient algorithm for maximum likelihood estimation (MLE) of
exponential family models, with a general parametrization of the energy
function that includes neural networks. We exploit the primal-dual view of the
MLE with a kinetics augmented model to obtain an estimate associated with an
adversarial dual sampler. To represent this sampler, we introduce a novel
neural architecture, dynamics embedding, that generalizes Hamiltonian
Monte-Carlo (HMC). The proposed approach inherits the flexibility of HMC while
enabling tractable entropy estimation for the augmented model. By learning both
a dual sampler and the primal model simultaneously, and sharing parameters
between them, we obviate the requirement to design a separate sampling
procedure once the model has been trained, leading to more effective learning.
We show that many existing estimators, such as contrastive divergence,
pseudo/composite-likelihood, score matching, minimum Stein discrepancy
estimator, non-local contrastive objectives, noise-contrastive estimation, and
minimum probability flow, are special cases of the proposed approach, each
expressed by a different (fixed) dual sampler. An empirical investigation shows
that adapting the sampler during MLE can significantly improve on
state-of-the-art estimators.Comment: Appearing in NeurIPS 2019 Vancouver, Canada; a preliminary version
published in NeurIPS2018 Bayesian Deep Learning Worksho
A N\'eel-type antiferromagnetic order in the spin 1/2 rare-earth honeycomb YbCl
Most of the searches for Kitaev materials deal with magnets with
spin-orbit-coupled local moments such as iridates and
-RuCl. Here we propose the monoclinic YbCl with a Yb
honeycomb lattice for the exploration of Kiteav physics. We perform
thermodynamic, susceptibility, angle-dependent magnetic torque and neutron
diffraction measurements on YbCl single crystal. We find that the Yb
ion exhibits a Kramers doublet ground state that gives rise to an effective
spin local moment. The compound exhibits short-range
magnetic order below 1.20 K, followed by a long-range N\'eel-type
antiferromagnetic order at 0.60 K, below which the ordered Yb spins lie
in the plane with an angle of 16(11) away from the axis.
These orders can be suppressed by in-plane and out-of-plane magnetic fields at
around 6 and 10 T, respectively. Moreover, the N\'eel temperature varies
non-monotonically under the out-of-plane magnetic fields. The in-plane magnetic
anisotropy and the reduced order moment 0.8(1) at 0.25 K indicate that
YbCl could be a two-dimensional spin system to proximate the Kitaev
physics.Comment: 6 pages, 5 figures, updated versio
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