2,715 research outputs found
Modular Matrices as Topological Order Parameter by Gauge Symmetry Preserved Tensor Renormalization Approach
Topological order has been proposed to go beyond Landau symmetry breaking
theory for more than twenty years. But it is still a challenging problem to
generally detect it in a generic many-body state. In this paper, we will
introduce a systematic numerical method based on tensor network to calculate
modular matrices in 2D systems, which can fully identify topological order with
gapped edge. Moreover, it is shown numerically that modular matrices, including
S and T matrices, are robust characterization to describe phase transitions
between topologically ordered states and trivial states, which can work as
topological order parameters. This method only requires local information of
one ground state in the form of a tensor network, and directly provides the
universal data (S and T matrices), without any non-universal contributions.
Furthermore it is generalizable to higher dimensions. Unlike calculating
topological entanglement entropy by extrapolating, which numerical complexity
is exponentially high, this method extracts a much more complete set of
topological data (modular matrices) with much lower numerical cost.Comment: 5+3 pages; 4+2 figures; One more appendix is adde
Entanglement entropy of (3+1)D topological orders with excitations
Excitations in (3+1)D topologically ordered phases have very rich structures.
(3+1)D topological phases support both point-like and string-like excitations,
and in particular the loop (closed string) excitations may admit knotted and
linked structures. In this work, we ask the question how different types of
topological excitations contribute to the entanglement entropy, or
alternatively, can we use the entanglement entropy to detect the structure of
excitations, and further obtain the information of the underlying topological
orders? We are mainly interested in (3+1)D topological orders that can be
realized in Dijkgraaf-Witten gauge theories, which are labeled by a finite
group and its group 4-cocycle up to group
automorphisms. We find that each topological excitation contributes a universal
constant to the entanglement entropy, where is the quantum
dimension that depends on both the structure of the excitation and the data
. The entanglement entropy of the excitations of the
linked/unlinked topology can capture different information of the DW theory
. In particular, the entanglement entropy introduced by Hopf-link
loop excitations can distinguish certain group 4-cocycles from the
others.Comment: 12 pages, 4 figures; v2: minor changes, published versio
QCD Glueball Masses from AdS-6 Black Hole Description
By using the generalized version of gauge/gravity correspondence, we study
the mass spectra of several typical QCD glueballs in the framework of
AdS black hole metric of Einstein gravity theory. The obtained glueball
mass spectra are numerically in agreement with those from the AdS
black hole metric of the 11-dimensional supergravity.Comment: 10 pages, references updated and minor change
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