# Complexity as a Novel Probe of Quantum Quenches: Universal Scalings and Purifications

Camargo, Hugo A. (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam-Golm, Germany) (Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany) ; Caputa, Pawel (Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan) ; Das, Diptarka (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam-Golm, Germany) ; Heller, Michal P. (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam-Golm, Germany) ; Jefferson, Ro (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam-Golm, Germany)

28 February 2019

Abstract: We apply the recently developed notion of complexity for field theory to a quantum quench through a critical point in $1+1$ dimensions. We begin with a toy model consisting of a quantum harmonic oscillator, and show that complexity exhibits universal scalings in both the slow and fast quench regimes. We then generalize our results to a one-dimensional harmonic chain, and show that preservation of these scaling behaviors in free field theory depends on the choice of norm. Applying our setup to the case of two oscillators, we quantify the complexity of purification associated with a subregion, and demonstrate 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.

Published in: Physical Review Letters 122 (2019)