Related papers: Universal relation for operator complexity

Universal relation for operator complexity

URL: http://arxiv.org/abs/2202.07220v3
Date: Tue, 14 Jun 2022 08:06:54 GMT
Title: Universal relation for operator complexity
Authors: Zhong-Ying Fan
Abstract summary: 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 $S_Ksim logC_K$ at long times, where dissipative behavior emerges in unitary evolution.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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.

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