Void formation in operator growth, entanglement, and unitarity

A bstract The structure of the Heisenberg evolution operators plays a key role in explaining diverse processes quantum many-body systems. In this paper, we discuss new universal feature operator evolution: an can develop void during its evolution, where nontrivial parts become separated by region identity operators. Such are present both integrable and chaotic systems, required unitarity. We show that formation has important implications for unitarity entanglement growth generation mutual information multipartite entanglement. study explicitly probability distributions number unitary circuit models, conjecture system distribution is given one find random circuits, which refer to as distribution. also circuits lead same pattern multiple intervals (1 + 1)-dimensional holographic CFTs after global quench, be used argue leads maximal growth.