Many-body quantum chaos and operator growth

4 problems

• Can a lattice with few states per site saturate the chaos bound

  Open

  Theory says scrambling at temperature $T$ cannot grow faster than the rate $2\pi k_{\mathrm{B}} T/\hbar$, and black holes and SYK reach this limit. Whether any laboratory material or ordinary lattice model in which each site holds only a few quantum states reaches it is unknown.

• Is energy diffusion bounded above by the butterfly velocity

  Partially resolved

  In some theories, how fast heat spreads is limited by how fast chaos spreads. Whether this limit holds in every chaotic lattice system is not settled.

• Asymptotic growth of Lanczos coefficients in one-dimensional chaotic chains

  Open

  The growth of an operator can be tracked by a sequence of numbers called Lanczos coefficients. In one dimension their exact large-order growth law is not established.

• Measured Lyapunov exponent versus temperature in a quantum simulator

  Open

  OTOC experiments so far probe effectively infinite-temperature states, where quantum limits on chaos do not show. Measuring the scrambling rate in a cold many-body state would test the chaos bound directly.