6,029 research outputs found
A relation between chiral central charge and ground state degeneracy in 2+1-dimensional topological orders
A bosonic topological order on -dimensional closed space may
have degenerate ground states. The space with different shapes
(different metrics) form a moduli space . Thus the
degenerate ground states on every point in the moduli space form a complex vector bundle over . It was
suggested that the collection of such vector bundles for -dimensional closed
spaces of all topologies completely characterizes the topological order. Using
such a point of view, we propose a direct relation between two seemingly
unrelated properties of 2+1-dimensional topological orders: (1) the chiral
central charge that describes the many-body density of states for edge
excitations (or more precisely the thermal Hall conductance of the edge), (2)
the ground state degeneracy on closed genus surface. We show that for bosonic topological orders. We explicitly
checked the validity of this relation for over 140 simple topological orders.
For fermionic topological orders, let ()
be the degeneracy with even (odd) number of fermions for genus- surface with
spin structure . Then we have and
for .Comment: 8 pages. This paper supersedes Section XIV of an unpublished work
arXiv:1405.5858. We add new results on fermionic topological orders and some
numerical check
A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
Topological orders are new phases of matter beyond Landau symmetry breaking.
They correspond to patterns of long-range entanglement. In recent years, it was
shown that in 1+1D bosonic systems there is no nontrivial topological order,
while in 2+1D bosonic systems the topological orders are classified by a pair:
a modular tensor category and a chiral central charge. In this paper, we
propose a partial classification of topological orders for 3+1D bosonic
systems: If all the point-like excitations are bosons, then such topological
orders are classified by unitary pointed fusion 2-categories, which are
one-to-one labeled by a finite group and its group 4-cocycle up to group automorphisms. Furthermore, all such 3+1D
topological orders can be realized by Dijkgraaf-Witten gauge theories.Comment: An important new result "Untwisted sector of dimension reduction is
the Drinfeld center of E" is added in Sec. IIIC; other minor refinements and
improvements; 23 pages, 10 figure
Field control of single x-ray photons in nuclear forward scattering
Means to coherently control single x-ray photons in resonant scattering of
light off nuclei by electric or magnetic fields are investigated theoretically.
In order to derive the time response in nuclear forward scattering, we adapt
the Maxwell-Bloch equations known from quantum optics to describe the resonant
light pulse propagation through a nuclear medium. Two types of time-dependent
perturbations of nuclear forward scattering are considered for coherent control
of the resonantly scattered x-ray quanta. First, the simultaneous coherent
propagation of two pulses through the nuclear sample is addressed. We find that
the signal of a weak pulse can be enhanced or suppressed by a stronger pulse
simultaneously propagating through the sample in counter-propagating geometry.
Second, the effect of a time-dependent hyperfine splitting is investigated and
we put forward a scheme that allows parts of the spectrum to be shifted forward
in time. This is the inverse effect of coherent photon storage and may become a
valuable technique if single x-ray photon wavepackets are to become the
information carriers in future photonic circuits.Comment: 21 pages, 10 figures, v2 minor modifications in text to match the
published version, results unchange
A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries
We propose that, up to invertible topological orders, 2+1D fermionic
topological orders without symmetry and 2+1D fermionic/bosonic topological
orders with symmetry are classified by non-degenerate unitary braided
fusion categories (UBFC) over a symmetric fusion category (SFC); the SFC
describes a fermionic product state without symmetry or a fermionic/bosonic
product state with symmetry , and the UBFC has a modular extension. We
developed a simplified theory of non-degenerate UBFC over a SFC based on the
fusion coefficients and spins . This allows us to obtain a list
that contains all 2+1D fermionic topological orders (without symmetry). We find
explicit realizations for all the fermionic topological orders in the table.
For example, we find that, up to invertible
fermionic topological orders, there
are only four fermionic topological orders with one non-trivial topological
excitation: (1) the
fractional quantum Hall state, (2) a Fibonacci bosonic topological order
stacking with a fermionic product state, (3) the time-reversal
conjugate of the previous one, (4) a primitive fermionic topological order that
has a chiral central charge , whose only topological excitation has
a non-abelian statistics with a spin and a quantum dimension
. We also proposed a categorical way to classify 2+1D invertible
fermionic topological orders using modular extensions.Comment: 23 pages, 8 table
On the "Security analysis and improvements of arbitrated quantum signature schemes"
Recently, Zou et al. [Phys. Rev. A 82, 042325 (2010)] pointed out that two
arbitrated quantum signature (AQS) schemes are not secure, because an
arbitrator cannot arbitrate the dispute between two users when a receiver
repudiates the integrity of a signature. By using a public board, they try to
propose two AQS schemes to solve the problem. This work shows that the same
security problem may exist in their schemes and also a malicious party can
reveal the other party's secret key without being detected by using the
Trojan-horse attacks. Accordingly, two basic properties of a quantum signature,
i.e. unforgeability and undeniability, may not be satisfied in their scheme
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