Physics

Quantum dynamics

Nonlinear system

Integrable system

Mathematical physics

Commutator

Quantum chaos

Artificial intelligence

Lyapunov exponent

Chaotic

Condensed matter physics

Spins

Computer science

Spin (aerodynamics)

Ising model

Lie algebra

Quantum mechanics

Observable

Lie conformal algebra

Quantum

Thermodynamics

Physical review. B./Physical review. B

The Ising spin chain with longitudinal and transverse magnetic fields is often used in studies of quantum chaos, displaying both chaotic and integrable regions in its parameter space. However, even at a strongly chaotic point this model does not exhibit Lyapunov growth of the commutator squared of spin operators, as this observable saturates before exponential growth can manifest itself (even in situations where a spatial suppression factor makes the initial commutator small). We extend this model from the spin 1/2 Ising model to higher spins, demonstrate numerically that a window of exponential growth opens up for sufficiently large spin, and extract a quantity which corresponds to a notion of a Lyapunov exponent. In the classical infinite-spin limit, we identify and compute the appropriate classical analogue of the commutator squared, and show that the corresponding exponent agrees with the infinite-spin limit extracted from the quantum spin chain.

Lyapunov growth in quantum spin chains