Diagnosing quantum chaos in many-body systems using entanglement
Classical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial state. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation functions (OTOCs). These quantities can be computed for various models, but their experimental study requires the ability to evolve quantum states backward in time, similar to the canonical Loschmidt echo measurement. In some simple systems, backward time evolution can be achieved by reversing the sign of the Hamiltonian; however in most interacting many-body systems, this is not a viable option. In this talk I will discuss a new family of protocols for OTOC measurement that do not require backward time evolution. Instead, they rely on ordinary time-ordered measurements performed in an entangled state formed between two identical copies of the system. I will show that, remarkably, in this situation the Lyapunov chaos exponent λ can be extracted from the measurement of an ordinary two-point correlation function under equilibrium conditions.