Universal relation for operator complexity

Abstract

We study Krylov complexity $C_K$ and operator entropy $S_K$ in operator growth. We find that for a variety of systems, including chaotic ones and integrable theories, the two quantities always enjoy a logarithmic relation $S_K\sim \log C_K$ at long times, where dissipative behavior emerges in unitary evolution. Otherwise, the relation does not hold any longer. Universality of the relation is deeply connected to irreversibility of operator growth.

Ppublication version.Minor revisions, conclusions unchanged. 22pages,4figures

References in corpus (3)

• Operator complexity: a journey to the edge of Krylov space
• Krylov complexity in conformal field theory
• Operator Delocalization in Quantum Networks

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