12,371 research outputs found
Ground state entanglement and geometric entropy in the Kitaev's model
We study the entanglement properties of the ground state in Kitaev's model.
This is a two-dimensional spin system with a torus topology and nontrivial
four-body interactions between its spins. For a generic partition of
the lattice we calculate analytically the von Neumann entropy of the reduced
density matrix in the ground state. We prove that the geometric
entropy associated with a region is linear in the length of its boundary.
Moreover, we argue that entanglement can probe the topology of the system and
reveal topological order. Finally, no partition has zero entanglement and we
find the partition that maximizes the entanglement in the given ground state.Comment: 4 pages, one fig, ReVTeX 4; updated to the published versio
Large Fourier transforms never exactly realized by braiding conformal blocks
Fourier transform is an essential ingredient in Shor's factoring algorithm.
In the standard quantum circuit model with the gate set \{\U(2),
\textrm{CNOT}\}, the discrete Fourier transforms , can be realized exactly by
quantum circuits of size , and so can the discrete
sine/cosine transforms. In topological quantum computing, the simplest
universal topological quantum computer is based on the Fibonacci
(2+1)-topological quantum field theory (TQFT), where the standard quantum
circuits are replaced by unitary transformations realized by braiding conformal
blocks. We report here that the large Fourier transforms and the discrete
sine/cosine transforms can never be realized exactly by braiding conformal
blocks for a fixed TQFT. It follows that approximation is unavoidable to
implement the Fourier transforms by braiding conformal blocks
Differential Renormalization of Massive Quantum Field Theories
We extend the method of differential renormalization to massive quantum field
theories treating in particular \ph4-theory and QED. As in the massless case,
the method proves to be simple and powerful, and we are able to find, in
particular, compact explicit coordinate space expressions for the finite parts
of two notably complicated diagrams, namely, the 2-loop 2-point function in
\ph4 and the 1-loop vertex in QED.Comment: 8 pages(LaTex, no figures
Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
For quantum field theories that flow between ultraviolet and infrared fixed
points, central functions, defined from two-point correlators of the stress
tensor and conserved currents, interpolate between central charges of the UV
and IR critical theories. We develop techniques that allow one to calculate the
flows of the central charges and that of the Euler trace anomaly coefficient in
a general N=1 supersymmetric gauge theory. Exact, explicit formulas for
gauge theories in the conformal window are given and analysed. The
Euler anomaly coefficient always satisfies the inequality .
This is new evidence in strongly coupled theories that this quantity satisfies
a four-dimensional analogue of the -theorem, supporting the idea of
irreversibility of the RG flow. Various other implications are discussed.Comment: latex, 27 page
Half-Life of O
We have measured the half-life of O, a superallowed decay isotope. The O was produced by the
C(He,n)O reaction using a carbon aerogel target. A
low-energy ion beam of O was mass separated and implanted in a thin
beryllium foil. The beta particles were counted with plastic scintillator
detectors. We find s. This result is
higher than an average value from six earlier experiments, but agrees more
closely with the most recent previous measurement.Comment: 10 pages, 5 figure
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