^{1,2}

^{,*}

^{3}

^{,†}

^{1}

^{,‡}

^{1}

^{,§}

^{1}

^{,∥}

On leave from National Centre for Nuclear Research, Hoża 69, 00-681 Warsaw, Poland.

^{3}.

We apply the recently developed notion of complexity for field theory to a quantum quench through a critical point in

Among the most exciting developments in theoretical physics is the confluence of ideas from quantum many-body systems, quantum information theory, and gravitational physics. Recent progress in this vein includes the development of tensor network methods for simulating quantum many-body systems (see, e.g., Ref.

However, insights from black hole physics

Drawing on earlier developments

To that end, one of the most active areas of research into nonequilibrium quantum dynamics is the study of quantum quenches

Motivated by these scaling phenomena, we explore the complexity of exact

Our interest in this setup is due to the fact that it can also be used to study the ground state of two (or more) harmonic oscillators with a time-dependent coupling. The same model was considered in Refs.

Given the form of Eq.

The details of our complexity calculation are given in Supplemental Material. The key point is that we may view

Since we are interested in the behavior of complexity as the system passes through the critical point of the quench, it is sufficient to evaluate this function at

Log-log plot of complexity of the (

Single-mode contributions to the complexity

The critical complexity of the zero mode

Zero-mode contribution to

One of the main motivations for the holographic complexity proposals was the observation that the information contained in the reduced density matrix of any spatial bipartition of the CFT Hilbert space, as encoded in the entanglement entropy, is generally insufficient to determine the entire bulk geometry

A particularly natural extension of existing pure-state definitions to this case is the

As observed in Fig.

Comparison of the complexity

Quenches represent tractable models of dynamical quantum systems in which complexity can be better understood, as well as yield new physical insights; e.g., we have found that complexity can be used to extract universal scalings. We have also examined the complexity of subregions (i.e., mixed states) via their purifications. Since complexity encodes global information about the state, it is sensitive to features to which entanglement is blind. We find that subregion complexity appears to satisfy superadditivity

We thank E. M. Brehm, S. R. Das, D. A. Galante, E. López, J. Magan, T. Takayanagi, M. Walter, and the co-authors of Ref.