PIRSA:19100075

Video URL

https://pirsa.org/19100075

A Universal Operator Growth Hypothesis

Scaffidi, T. (2019). A Universal Operator Growth Hypothesis. Perimeter Institute for Theoretical Physics. https://pirsa.org/19100075

Scaffidi, Thomas. A Universal Operator Growth Hypothesis. Perimeter Institute for Theoretical Physics, Oct. 15, 2019, https://pirsa.org/19100075 

          @misc{ scivideos_PIRSA:19100075,
            doi = {10.48660/19100075},
            url = {https://pirsa.org/19100075},
            author = {Scaffidi, Thomas},
            keywords = {Quantum Matter},
            language = {en},
            title = {A Universal Operator Growth Hypothesis},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {oct},
            note = {PIRSA:19100075 see, \url{https://scivideos.org/index.php/pirsa/19100075}}
          }

Thomas Scaffidi University of Toronto

Talk numberPIRSA:19100075
DOI10.48660/19100075
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Thanks to the Lanczos algorithm, the Hamiltonian dynamics of any operator can be written as a hopping problem on a semi-infinite one-dimensional chain. Our hypothesis states that the hopping strength grows linearly down the chain, with a universal growth rate $\alpha$ that is an intrinsic property of the system. This leads to an exponential motion of the operator down the chain, capturing the irreversible process of simple operators inevitably evolving into complex ones. This exponential growth exists for generic quantum systems, even away from large-$N$ or semiclassical limits. In fact, $\alpha$ gives an upper bound for the exponential growth rate of a large class of operator complexity measures, including out-of-time-order correlations. As a result, we conjecture a new bound on Lyapunov exponents $\lambda_L \leq 2 \alpha$, which generalizes the known universal low-temperature bound $\lambda_L \leq 2 \pi T$. We illustrate the hypothesis in paradigmatic examples such as non-integrable spin chains, the $q$-SYK model, and chaotic coupled top models, and show that some of them saturate the conjectured bound.