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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 4: Quantum field theory, AdS/CFT, non-equilibrium and quantum dynamics

MP 4.2: Talk

Tuesday, March 22, 2022, 16:35–16:55, MP-H5

Quantum Complexity as Hydrodynamics — •Pablo Basteiro^1,2, Johanna Erdmenger^1,2, Pascal Fries¹, Florian Goth^1,2, Ioannis Matthaiakakis^1,2, and René Meyer^1,2 — ¹Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany — ²Würzburg-Dresden Cluster of Excellence ct.qmat

In recent years, many concepts of quantum information theory have been introduced to the AdS/CFT correspondence and have lead to several meaningful insights. In particular, quantum computational complexity has been suggested as a candidate to describe the late-time behavior of black hole interiors. We contribute to its understanding by considering Nielsen’s geometric approach to operator complexity for the SU(N) group. We develop a tractable large N limit which leads to regular geometries on the manifold of unitaries. To achieve this, we introduce a particular basis for the su(N) algebra and define a maximally anisotropic metric with polynomial penalty factors. We implement the Euler-Arnold approach to identify incompressible inviscid hydrodynamics on the two-torus as a novel effective theory for the evaluation of operator complexity of large qudits. We discuss the resulting complexity geometry in view of essential properties of holographic complexity measures, such as ergodicity and conjugate points.