Bonn 2020 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: AdS/CFT: Complexity

MP 11.1: Talk

Wednesday, April 1, 2020, 14:15–14:35, H-HS I

Complexity for Quantum Fields: Subregions, Mixed States and Purifications — •Hugo Antonio Camargo Montero — Albert Einstein Institute, Potsdam, Germany

In this talk we explore the notion of complexity in quantum field theories. We first apply the notion of circuit complexity to a quantum quench through a critical point in 1+1 dimensions. We apply this setup to a Gaussian state with two degrees of freedom, where we quantify the complexity of purification associated with a subregion, and show that complexity is capable of probing features to which the entanglement entropy is insensitive. We find that the complexity of subregions is subadditive, and comment on potential implications for holography. We also discuss upcoming work regarding the study of complexity of purification for mixed Gaussian states with a large number of degrees of freedom. In the second part of the talk, we enter the recent discussion involving the two definitions of complexity in field theories, namely circuit complexity and path integral complexity. We focus on two-dimensional conformal field theories (CFTs) where we provide a measure for the circuit complexity associated to the unnormalized thermal density matrix ρ=exp(−β H). We show that the Liouville action, which is the path integral complexity measure for ρ, is an approximation to a genuine circuit complexity measure.