Holographic Complexity and Charged Scalar Fields
arXiv:1902.01912 · doi:10.1103/PhysRevD.99.106013
Abstract
We construct a time-dependent expression of the computational complexity of a quantum system which consists of two conformal complex scalar field theories in d dimensions coupled to constant electric potentials and defined on the boundaries of a charged AdS black hole in (d+1) dimensions. Using a suitable choice of the reference state, Hamiltonian gates and the metric on the manifold of unitaries, we find that the complexity grows linearly for a relatively large interval of time. We also remark that for scalar fields with very small charges the rate of variation of the complexity cannot exceed a maximum value known as the Lloyd bound.
9 pages, 2 figures, typos corrected from earlier version, reference added