Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos

Journal article

The exponential growth or decay with time of the out-of-time-order commutator (OTOC) is one widely used diagnostic of many-body chaos in spatially extended systems. In studies of many-body classical chaos, it has been noted that one can define a velocity-dependent Lyapunov exponent, λ(v), which is the growth or decay rate along rays at that velocity. We examine the behavior of λ(v) for a variety of many-body systems, both chaotic and integrable. The so-called light cone for the spreading of operators is defined by λ(ˆnvB(ˆn))=0, with a generally direction-dependent butterfly speed vB(ˆn). In spatially local systems, λ(v) is negative outside the light cone where it takes the form λ(v)∼−(v−vB)α near vB, with the exponent α taking on various values over the range of systems we examine. The regime inside the light cone with positive Lyapunov exponents may only exist for classical, semiclassical, or large-N systems, but not for “fully quantum” chaotic systems with strong short-range interactions and local Hilbert space dimensions of order one.

Authors: Khemani, V; Huse, D; Nahum, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review B
• Volume: 98
• Issue: 14
• Article number: 144304
• Publication date: 2018-10-16
• Acceptance date: 2018-09-26
• DOI: 10.1103/PhysRevB.98.144304
• EISSN: 2469-9969
• ISSN: 2469-9950