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• W3106169596 abstract "Motivated by holographic complexity proposals as novel probes of black hole spacetimes, we explore circuit complexity for thermofield double (TFD) states in free scalar quantum field theories using the Nielsen approach. For TFD states at t = 0 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> , we show that the complexity of formation is proportional to the thermodynamic entropy, in qualitative agreement with holographic complexity proposals. For TFD states at t>0 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>t</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> , we demonstrate that the complexity evolves in time and saturates after a time of the order of the inverse temperature. The latter feature, which is in contrast with the results of holographic proposals, is due to the Gaussian nature of the TFD state of the free bosonic QFT. A novel technical aspect of our work is framing complexity calculations in the language of covariance matrices and the associated symplectic transformations, which provide a natural language for dealing with Gaussian states. Furthermore, for free QFTs in 1+1 dimension, we compare the dynamics of circuit complexity with the time dependence of the entanglement entropy for simple bipartitions of TFDs. We relate our results for the entanglement entropy to previous studies on non-equilibrium entanglement evolution following quenches. We also present a new analytic derivation of a logarithmic contribution due to the zero momentum mode in the limit of vanishing mass for a subsystem containing a single degree of freedom on each side of the TFD and argue why a similar logarithmic growth should be present for larger subsystems." @default.
• W3106169596 created "2020-11-23" @default.
• W3106169596 creator A5007704969 @default.
• W3106169596 creator A5016178100 @default.
• W3106169596 creator A5030304574 @default.
• W3106169596 creator A5039471780 @default.
• W3106169596 creator A5041824947 @default.
• W3106169596 creator A5048013785 @default.
• W3106169596 creator A5077663153 @default.
• W3106169596 date "2019-03-15" @default.
• W3106169596 modified "2023-10-16" @default.
• W3106169596 title "Complexity and entanglement for thermofield double states" @default.
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