Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series SEM-CPHT
Subjects hep-th
Date Tuesday 11 February 2020
Time 11:00
Institute CPHT
Seminar Room Salle Louis Michel
Speaker's Last Name Kim
Speaker's First Name Keun-Young
Speaker's Email Address
Speaker's Institution GIST
Title Comments on (Operator) Complexity
Abstract Many concepts of the quantum information theory have been widely applied to the studies of quantum fields and gravity. In particular, “complexity”, a concept originated from the quantum circuits and quantum computations, has been introduced to the studies of black hole physics and the gauge/gravity duality. Roughly speaking, from the perspective of the quantum circuit, the complexity of an operator (circuit) is the minimal number of “elementary operations" (gates) to construct a specific operator (circuit). Although there has been much progress on the "holographic" complexity in the gravity side, such as the complexity- volume (CV) conjecture and the complexity-action (CA) conjecture, the precise definition of the complexity in the field theory side is still incomplete. We introduce how to define the complexity of an operator in the field theory based on minimal properties of the circuit complexity and general principles of field theory. We follow Nielsen's idea of complexity geometry and geodesics thereof. As an example, we investigate the time evolution of the complexity of the operator by the Sachdev-Ye-Kitaev (SYK) model with N Majorana fermions. We show that it is possible that our complexity geometry can exhibit the conjectured time evolution of the complexity in chaotic systems: i) linear growth until t~eN, ii) saturation and small fluctuations after then.
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