75,133 research outputs found
ON THE 82-TH SMARANDACHE’S PROBLEM
The main purpose of this paper is using the elementary method to study the asymptotic properties of the integer part of the k-th root positive integer, and give two interesting asymptotic formulae
The Ringel--Hall Lie algebra of a spherical object
For an integer , let \cs_w be the algebraic triangulated category
generated by a -spherical object. We determine the Picard group of \cs_w
and show that each orbit category of \cs_w is triangulated and is triangle
equivalent to a certain orbit category of the bounded derived category of a
standard tube. When , the orbit category \cs_w/\Sigma^2 is 2-periodic
triangulated, and we characterize the associated Ringel--Hall Lie algebra in
the sense of Peng and Xiao.Comment: 26page
Detecting crystal symmetry fractionalization from the ground state: Application to spin liquids on the kagome lattice
In quantum spin liquid states, the fractionalized spinon excitations can
carry fractional crystal symmetry quantum numbers, and this symmetry
fractionalization distinguishes different topologically ordered spin liquid
states. In this work we propose a simple way to detect signatures of such
crystal symmetry fractionalizations from the crystal symmetry representations
of the ground state wave function. We demonstrate our method on projected
spin liquid wave functions on the kagome lattice, and show that
it can be used to classify generic wave functions. Particularly our method can
be used to distinguish several proposed candidates of spin liquid
states on the kagome lattice.Comment: main text: 6 pages, 1 figure. supplemental material: 8 pages, 2
figures. Added a few references and the journal referenc
Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators
The surface of a three-dimensional topological electron system often hosts
symmetry-protected gapless surface states. With the effect of electron
interactions, these surface states can be gapped out without symmetry breaking
by a surface topological order, in which the anyon excitations carry anomalous
symmetry fractionalization that cannot be realized in a genuine two-dimensional
system. We show that for a mirror-symmetry-protected topological crystalline
insulator with mirror Chern number , its surface can be gapped out by an
anomalous topological order, where all anyons carry
mirror-symmetry fractionalization . The identification of such
anomalous crystalline symmetry fractionalization implies that in a
two-dimensional spin liquid the vison excitation cannot carry
if the spinon carries or a half-integer spin.Comment: 6+8 pages, 2 figures. v2: added a new section in the supplemental
material, the journal reference and some other change
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