Information propagation in isolated quantum systems

By D. J. Luitz, Yevgeny Bar Lev. 2017

152 citations recorded by the source corpus.

Entanglement growth and out-of-time-order correlators (OTOC) are used to assess the propagation of information in isolated quantum systems. In this work, using large scale exact time-evolution we show that for weakly disordered nonintegrable systems information propagates behind a ballistically moving front, and the entanglement entropy growths linearly in time. For stronger disorder the motion of the information front is algebraic and sub-ballistic and is characterized by an exponent which depends on the strength of the disorder, similarly to the sublinear growth of the entanglement entropy. We show that the dynamical exponent associated with the information front coincides with the exponent of the growth of the entanglement entropy for both weak and strong disorder. We also demonstrate that the temporal dependence of the OTOC is characterized by a fast\emph onnonexponential\emph default growth, followed by a slow saturation after the passage of the information front. Finally,we discuss the implications of this behavioral change on the growth of the entanglement entropy.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/887ac53a9b620c4ed97682675876732f19412240

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. V. Khemani
3. Shenglong Xu
4. Brian Swingle
5. D. Huse
6. S. Vijay
7. Matthew Fisher
8. Frank Pollmann

In Statistical and Nonlinear Physics

1. A. Nahum
2. Shenglong Xu
3. V. Khemani
4. Brian Swingle
5. S. Vijay
6. D. Huse
7. Frank Pollmann
8. Tibor Rakovszky

Citations in the corpus

• Operator Spreading in Random Unitary Circuits (2017, background): “This region typically grows ballistically [58], even when local conserved quantities exhibit diffusive transport [31,38,49,50,59].”
• Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, background): “an intermediate time diagnostic of quantum chaos is an open question (one interesting quantity is the operator entanglement of a spreading operator, which at least in some integrable systems [56–58] grows much slower than in chaotic systems [36, 59].”
• Locality, Quantum Fluctuations, and Scrambling (2018, background): “[33] D.”
• Engineered dissipation for quantum information science (2022, background): “Deep insight is being developed into the connections between classical and quantum chaos 266 , how information propagates in a quantum system 267 , and the interplay between coherent and incoherent processes in the propagation of entanglement 268,269 .”
• Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation (2017, background): “This overlap approximates the infinite temperature average up to an error which is exponentially small in the system size [23], and we indeed find numerically that the deviation of the OTOC between different random states is negligible at the system sizes we consider.”
• Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws (2017, background): “It is known, for example, that the propagation of the OTOC becomes slower than ballistic in strongly disordered (but still thermalizing) systems [65], and it is an interesting question whether this effect can be incorporated into some form of hydrodynamic description.”