Abstract
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.
Highlights
Over the past years, the AdS/conformal field theory (CFT) correspondence [1, 2, 3] has been extensively applied to the study of superconductor/superfluid in condensed matter physics
Considering the thermal entropy is equivalent to the black hole entropy in the holographic setup, our results indicate that the black hole entropy could be due to the entanglement entropy [28, 29, 30, 31]
The second order, first order and even zeroth order phase transitions would appear in this model and the so-called “retrograde condensation” could happen in some parameter space
Summary
The AdS/CFT correspondence [1, 2, 3] has been extensively applied to the study of superconductor/superfluid in condensed matter physics. Comparing the holographic p-wave model by introducing a SU(2) gauge field in the bulk proposed in ref. [17, 18, 19, 20, 21] studied the behaviors of entanglement entropy in holographic conductor/superconductor phase transition, including s-wave and p-wave cases. The behaviors of entanglement entropy for the holographic s-wave and p-wave superconductor/insulator model at zero temperature have been investigated in refs. We will study the entanglement entropy in this new holographic p-wave superconductor model [9, 10]. We have the equations of motion for gauge field Aμ and charged vector field ρμ as
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