Entanglement Membrane in Chaotic Many-Body Systems

By Tianci Zhou, A. Nahum. 2019

144 citations recorded by the source corpus.

In certain analytically-tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables, reduces to an effective theory of an ``entanglement membrane'' in spacetime. These tractable systems involve an average over random local unitaries defining the dynamical evolution. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries. Our approach relies on introducing effective pairing degrees of freedom in spacetime, describing a pairing of forward and backward Feynman trajectories, inspired by the structure emerging in random unitary circuits. This provides a framework for applying ideas of coarse-graining to dynamical quantities in chaotic systems. We apply the approach to some translationally invariant Floquet spin chains studied in the literature. We show that a consistent line tension may be defined for the entanglement membrane, and that there are qualitative differences in this tension between generic models and ``dual-unitary'' circuits. These results allow scaling pictures for out-of-time-order correlators and for entanglement to be taken over from random circuits to non-random Floquet models. We also provide an efficient numerical algorithm for determining the entanglement line tension in 1+1D.

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

View Paper: https://www.semanticscholar.org/paper/ca0af477711af6acde12bcfe8685ea8b68c016a5

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. Matthew Fisher
2. A. Nahum
3. V. Khemani
4. B. Skinner
5. J. Ruhman
6. S. Vijay
7. Sthitadhi Roy
8. D. Huse

In Statistical and Nonlinear Physics

1. A. Nahum
2. J. Ruhman
3. B. Skinner
4. Sthitadhi Roy
5. S. Vijay
6. Matthew Fisher
7. V. Khemani

Citations in the corpus

• Random Quantum Circuits (2022, background): “Loosely speaking, randomness in a quantum circuit allows for a classical description of the evolving entanglement structure in a typical realization of the quantum many-body dynamics (16, 49, 50, 51).”
• Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, methodology): “Heuristically, pairing Feynman histories in the discrete time evolution allows phase cancellation to be avoided [33, 42], in the spirit of the diagonal approximation in periodic orbit theory [85].”