Out-of-time-ordered correlators in a quantum Ising chain
By Cheng-Ju Lin, O. Motrunich. 2018
159 citations recorded by the source corpus.
Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a “shell-like” structure: After the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a t^(−1) power law at long time t. On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a “ball-like” structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law t^(−1/4) for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not captured by conformal field theory calculations. The mixed OTOC with both local and nonlocal operators in the Jordan-Wigner fermions also has a “ball-like” structure, but the limiting values and the decay behavior appear to be nonuniversal. In all cases, we are not able to define a parametrically large window around the wavefront to extract the Lyapunov exponent.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/70d0edd1b96b2c03544fc8b20cc49f7bb708774a
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
- V. Khemani
- A. Nahum
- Shenglong Xu
- D. Huse
- Brian Swingle
- Matthew Fisher
- Tianci Zhou
- Nicholas Hunter-Jones
In Statistical and Nonlinear Physics
Citations in the corpus
- Locality, Quantum Fluctuations, and Scrambling (2018, background): “[36] C.”
- Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, background): “We note, however, that the late-time behavior of the OTOC (inside the light cone) is operator dependent and can decay to zero in non-interacting models [39]”
- Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, background): “For a generic system with short-ranged interaction and no disorder, local operators spread ballistically, which has been shown in numerous systems including field theories [54, 55], free and integrable models [56, 57], interacting spin chains [58, 59] and circuit models [60–63].”