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Exact solutions to the time-dependent supersymmetric muliphoton Jaynes-Cummings model and the Chiao-Wu model
By using both the Lewis-Riesenfeld invariant theory and the invariant-related
unitary transformation formulation, the present paper obtains the exact
solutions to the time-dependent supersymmetric two-level multiphoton
Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of
a photon inside the optical fiber. On the basis of the fact that the two-level
multiphoton Jaynes-Cummings model possesses the supersymmetric structure, an
invariant is constructed in terms of the supersymmetric generators by working
in the sub-Hilbert-space corresponding to a particular eigenvalue of the
conserved supersymmetric generators (i.e., the time-independent invariant). By
constructing the effective Hamiltonian that describes the interaction of the
photon with the medium of the optical fiber, it is further verified that the
particular solution to the Schr\"{o}dinger equation is the eigenfunction of the
second-quantized momentum operator of photons field. This, therefore, means
that the explicit expression (rather than the hidden form that involves the
chronological product) for the time-evolution operator of wave function is
obtained by means of the invariant theories.Comment: 14 pages, Latex. This is a revised version of the published paper:
Shen J Q, Zhu H Y 2003 Ann. Phys.(Leipzig) Vol.12 p.131-14
Entanglement entropy and entanglement spectrum of the Kitaev model
In this paper, we obtain an exact formula for the entanglement entropy of the
ground state and all excited states of the Kitaev model. Remarkably, the
entanglement entropy can be expressed in a simple separable form S=S_G+S_F,
with S_F the entanglement entropy of a free Majorana fermion system and S_G
that of a Z_2 gauge field. The Z_2 gauge field part contributes to the
universal "topological entanglement entropy" of the ground state while the
fermion part is responsible for the non-local entanglement carried by the Z_2
vortices (visons) in the non-Abelian phase. Our result also enables the
calculation of the entire entanglement spectrum and the more general Renyi
entropy of the Kitaev model. Based on our results we propose a new quantity to
characterize topologically ordered states--the capacity of entanglement, which
can distinguish the states with and without topologically protected gapless
entanglement spectrum.Comment: 4.0 pages + supplementary material, published version in Phys. Rev.
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