Complexity of Holographic Superconductors
Feb 20, 2019
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Abstract: (Springer)
We study the complexity of holographic superconductors (Einstein-Maxwell-complex scalar actions in d + 1 dimension) by the “complexity = volume” (CV) conjecture. First, it seems that there is a universal property: the superconducting phase always has a smaller complexity than the unstable normal phase below the critical temperature, which is similar to a free energy. We investigate the temperature dependence of the complexity. In the low temperature limit, the complexity (of formation) scales as T, where α is a function of the complex scalar mass m, the U(1) charge q, and dimension d. In particular, for m = 0, we find α = d−1, independent of q, which can be explained by the near horizon geometry of the low temperature holographic superconductor. Next, we develop a general numerical method to compute the time-dependent complexity by the CV conjecture. By this method, we compute the time-dependent complexity of holographic superconductors. In both normal and superconducting phase, the complexity increases as time goes on and the growth rate saturates to a temperature dependent constant. The higher the temperature is, the bigger the growth rate is. However, the growth rates do not violate the Lloyd’s bound in all cases and saturate the Lloyd’s bound in the high temperature limit at a late time.Note:
- a minor modification on the discussions of mass without changing the main results; references added
- Gauge-gravity correspondence
- Holography and condensed matter physics (AdS/CMT)
- superconductivity: holography
- temperature: high
- temperature: low
- horizon: geometry
- mass: scalar
- temperature dependence
- time dependence
- critical phenomena
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