Two-step phantom relaxation of out-of-time-ordered correlations in random circuits

• URL: http://arxiv.org/abs/2112.07281v2
• Date: Thu, 31 Mar 2022 06:59:04 GMT
• Title: Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
• Authors: Jas Bensa and Marko Znidaric
• Abstract summary: We study out-of-time-ordered correlation functions in various random quantum circuits. We show that the average dynamics is governed by a Markovian propagator.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study out-of-time-ordered correlation (OTOC) functions in various random quantum circuits and show that the average dynamics is governed by a Markovian propagator. This is then used to study relaxation of OTOC to its long-time average value in circuits with random single-qubit unitaries, finding that relaxation in general proceeds in two steps: in the first phase that lasts upto an extensively long time the relaxation rate is given by a phantom eigenvalue of a non-symmetric propagator, whereas in the second phase the rate is determined by the true 2nd largest propagator eigenvalue. We also obtain exact OTOC dynamics on the light-cone and an expression for the average OTOC in finite random circuits with random two-qubit gates.

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