Berlin 2018 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 54: Focus Session: Chaos and Correlation in Quantum Matter (joint session DY/TT)
TT 54.2: Talk
Wednesday, March 14, 2018, 10:00–10:15, EB 107
Hydrodynamics of operator spreading from random circuits — •Tibor Rakovszky1, Curt von Keyserlingk2, Shivaji Sondhi3, and Frank Pollmann1 — 1Department of Physics, T42, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany — 2University of Birmingham, School of Physics & Astronomy, B15 2TT, UK — 3Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
In this talk we use random local unitary circuits to gain insight into the scrambling of quantum information in many-body systems. For a circuit with no conserved quantities we show that the average spreading of operators obeys an exact "hydrodynamic" description, in terms of a biased diffusion equation, and discuss the consequences for out-of-time ordered correlators (OTOCs) and entanglement growth. We conjecture that a similar effective description should hold in more generic ergodic systems, a claim supported by numerical results. Furthermore, we consider random circuits with a U(1) symmetry and discuss the interplay between the hydrodynamics of the conserved charge and that of operator spreading, leading to the appearance of long-time power law tails in out-of-time-ordered correlators. We also discuss the behavior of OTOCs at different chemical potentials, an analogous quantity to the finite temperature OTOCs discussed in the literature, and find that their initial spreading is slowed down when the chemical potential is large.