4,957 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 This paper supersedes Section XIV of an unpublished work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 channel Brownian pump powered by an unbiased external force
A Brownian pump of particles in an asymmetric finite tube is investigated in
the presence of an unbiased external force. The pumping system is bounded by
two particle reservoirs. It is found that the particles can be pumped through
the tube from a reservoir at low concentration to one at the same or higher
concentration. There exists an optimized value of temperature (or the amplitude
of the external force) at which the pumping capacity takes its maximum value.
The pumping capacity decreases with increasing the radius at the bottleneck of
the tube.Comment: 14 pages, 9 figure
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
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