Johanna Erdmenger, Mario Flory, Marius Gerbershagen, Michal P. Heller, AnnaLena Weigel
SciPost Phys. 13, 061 (2022) ·
published 22 September 2022

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Holographic complexity proposals have sparked interest in quantifying the cost of state preparation in quantum field theories and its possible dual gravitational manifestations. The most basic ingredient in defining complexity is the notion of a class of circuits that, when acting on a given reference state, all produce a desired target state. In the present work we build on studies of circuits performing local conformal transformations in general twodimensional conformal field theories and construct the exact gravity dual to such circuits. In our approach to holographic complexity, the gravity dual to the optimal circuit is the one that minimizes an externally chosen cost assigned to each circuit. Our results provide a basis for studying exact gravity duals to circuit costs from first principles.
Michal P. Heller, Alexandre Serantes, Michał Spaliński, Viktor Svensson, Benjamin Withers
SciPost Phys. 10, 123 (2021) ·
published 1 June 2021

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We study the mechanisms setting the radius of convergence of hydrodynamic
dispersion relations in kinetic theory in the relaxation time approximation.
This introduces a qualitatively new feature with respect to holography: a
nonhydrodynamic sector represented by a branch cut in the retarded Green's
function. In contrast with existing holographic examples, we find that the
radius of convergence in the shear channel is set by a collision of the
hydrodynamic pole with a branch point. In the sound channel it is set by a
polepole collision on a nonprincipal sheet of the Green's function. More
generally, we examine the consequences of the implicit function theorem in
hydrodynamics and give a prescription to determine a set of points that
necessarily includes all complex singularities of the dispersion relation. This
may be used as a practical tool to assist in determining the radius of
convergence of hydrodynamic dispersion relations.
Shira Chapman, Jens Eisert, Lucas Hackl, Michal P. Heller, Ro Jefferson, Hugo Marrochio, Robert C. Myers
SciPost Phys. 6, 034 (2019) ·
published 15 March 2019

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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, 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, 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
nonequilibrium 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.