Work

Operator dynamics in a Brownian quantum circuit

Year: 2019

Type: article

Abstract: We view the operator spreading in chaotic evolution as a stochastic process of height growth. The height of an operator represents the size of its support and chaotic evolution increases the height. We consider N-spin models with all two-body interactions and embody the height picture in a random model. The exact solution shows that the mean height, being proportional to the squared commutator, grows exponentially within logN scrambling time and saturates in a manner of logistic function. We propose that the temperature dependence of the chaos bound could be due to initial height biased toward high operators, which has a smaller Lyapunov exponent.

Source: Physical review. E

DOI: 10.1103/physreve.99.052212

Authors: Tianci Zhou, Xiao Chen

Institutions: University of California, Santa Barbara, University of Illinois Urbana-Champaign, Kavli Institute for Theoretical Physics

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Gordon and Betty Moore Foundation, Kavli Institute for Theoretical Physics, University of California, Santa Barbara

Awards: Moore Scholars in Theory of Quantum Materials, Materials Research Science and Engineering Center at UCSB