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
References in corpus (25)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Eternal Black Holes in AdS
- Charged AdS Black Holes and Catastrophic Holography
- Black holes as mirrors: quantum information in random subsystems
- Fast Scramblers
- Time Optimal Control in Spin Systems
- Complexity, action, and black holes
- Circuit complexity in quantum field theory
- Towards Complexity for Quantum Field Theory States
- Gravitational action with null boundaries
- Charged and rotating AdS black holes and their CFT duals
- Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
- On the Time Dependence of Holographic Complexity
- Complexity of Formation in Holography
- Entanglement renormalization for quantum fields
- Complexity and entanglement for thermofield double states
- Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
- Gravity Dual of Quantum Information Metric
- Large N Phases, Gravitational Instantons and the Nuts and Bolts of AdS Holography
- Time Evolution of Complexity: A Critique of Three Methods
- Evolution of Complexity Following a Global Quench
- Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature
- Evolution of complexity following a quantum quench in free field theory
- Divergences in the rate of complexification
- Topological and Time Dependence of the Action-Complexity Relation
Cited by in corpus (14)
- Black Hole Chemistry: the first 15 years
- Charged Complexity and the Thermofield Double State
- More on Complexity in Finite Cut Off Geometry
- Revisit on holographic complexity in two-dimensional gravity
- Circuit complexity in proca theory
- Reparameterization Dependence is Useful for Holographic Complexity
- Complexity growth for topological black holes by holographic method
- Complexity from Spinning Primaries
- Weighting gates in circuit complexity and holography
- Generalized holographic complexity of rotating black holes
- Complexity for superconformal primaries from BCH techniques
- Reparameterization Dependence and Holographic Complexity of Black Holes
- D5-brane on topological black holes
- Holographic complexity of rotating black holes