Experimental progress in atomic, molecular, and optical platforms in the last decade has
stimulated strong and broad interest in the quantum coherent dynamics of many long-range …

We derive field theory descriptions for measurement-induced phase transitions in free
fermion systems. We focus on a multiflavor Majorana chain, undergoing Hamiltonian …

We construct Brownian Sachdev-Ye-Kitaev (SYK) chains subjected to continuous monitoring
and explore possible entanglement phase transitions therein. We analytically derive the …

This tutorial article introduces the physics of quantum information scrambling in quantum
many-body systems. The goals are to understand how to precisely quantify the spreading of …

We show that out-of-time-order correlators (OTOCs) constitute a probe for local-operator
entanglement (LOE). There is strong evidence that a volumetric growth of LOE is a faithful …

Entanglement is one of the most important concepts in quantum physics. We review recent
progress in understanding the quantum entanglement in many-body systems using large-N …

Quantum thermalization in a many-body system is defined by the approach of local
subsystems toward a universal form, describable as an ensemble of quantum states wherein …

Unitary designs have become a vital tool for investigating pseudorandomness, since they
approximate the statistics of the uniform Haar ensemble. Despite their central role in …

We study the operator growth problem and its complexity in the many-body localization
(MBL) system from the Lanczos algorithm perspective. Using the Krylov basis, the operator …

The entanglement in operator space is a well established measure for the complexity of the
quantum many-body dynamics. In particular, that of local operators has recently been …