Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation
By Tibor Rakovszky, Frank Pollmann, C. V. von Keyserlingk. Physical Review X, 2017
358 citations recorded by the source corpus.
The scrambling of quantum information in closed many-body systems has received considerable recent attention. Two useful measures of scrambling have emerged: the spreading of initially-local operators, and the related concept of out-of-time-ordered correlation functions (OTOCs). Recently, random circuits have been used to give these quantities an effective hydrodynamical description. We extend these results by considering local random unitary circuits with a conserved U$(1)$ charge and argue, with numerical and analytical evidence, that the presence of a conservation law slows relaxation in both time ordered and time-out-of ordered correlation functions; we show that both can have a diffusively relaxing component or "power-law tail" at late times. Moreover, we consider OTOCs in Gibbs states, parametrized by a chemical potential $\mu$, and apply perturbative arguments to show that for $\mu\gg 1$ the ballistic front of information-spreading can only develop at times exponentially large in $\mu$ -- with the information traveling diffusively at earlier times. We also develop a new formalism for describing OTOCs and operator spreading, which allows us to describe the saturation of OTOCs as a form of "thermalization on operator space", and leads to a conjecture for their long-time behavior, wherein the conservation law results in a particular profile for OTOCs, showing a slow decay behind the main front. Our results may be relevant to systems with energy conservation, with the role of chemical potential played by the inverse temperature, even though our models explicitly break time translation symmetry.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/282c26918c05979742b2872af858bf47f5790b38
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Citations in the corpus
- Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “) Results on random circuits with conservation laws provide a starting point [9, 10].”
- Unitary circuits of finite depth and infinite width from quantum channels (2019, methodology): “[33] Tibor Rakovszky, Frank Pollmann, and C.”
- Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, background): “There are also generalizations of the random unitary circuit to respect charge conservation [74, 75], dipolar conservation [76] or other kinetic constraints, which are important for studying the interplay between transport phenomena and scrambling.”