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A Holographic P-wave Superconductor Model
We study a holographic p-wave superconductor model in a four dimensional
Einstein-Maxwell-complex vector field theory with a negative cosmological
constant. The complex vector field is charged under the Maxwell field. We solve
the full coupled equations of motion of the system and find black hole
solutions with the vector hair. The vector hairy black hole solutions are dual
to a thermal state with the U(1) symmetry as well as the spatial rotational
symmetry breaking spontaneously. Depending on two parameters, the mass and
charge of the vector field, we find a rich phase structure: zeroth order, first
order and second order phase transitions can happen in this model. We also find
"retrograde condensation" in which the hairy black hole solution exists only
for the temperatures above a critical value with the free energy much larger
than the black hole without hair. We construct the phase diagram for this
system in terms of the temperature and charge of the vector field.Comment: v3: 26 pages, 15 figures, references added, extra arguments added, to
appear in JHE
Entanglement entropy in a holographic p-wave superconductor model
In a recent paper, arXiv:1309.4877, a holographic p-wave model has been
proposed in an Einstein-Maxwell-complex vector field theory with a negative
cosmological constant. The model exhibits rich phase structure depending on the
mass and the charge of the vector field. We investigate the behavior of the
entanglement entropy of dual field theory in this model. When the above two
model parameters change, we observe the second order, first order and zeroth
order phase transitions from the behavior of the entanglement entropy at some
intermediate temperatures. These imply that the entanglement entropy can
indicate not only the occurrence of the phase transition, but also the order of
the phase transition. The entanglement entropy is indeed a good probe to phase
transition. Furthermore, the "retrograde condensation" which is a sub-dominated
phase is also reflected on the entanglement entropy.Comment: figures added; accepted by Nuclear Physics
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