Quantum chaos in an electron-phonon bad metal

Understand

We calculate the scrambling rate $\lambda_L$ and the butterfly velocity $v_B$ associated with the growth of quantum chaos for a solvable large-$N$ electron-phonon system.

• We study a temperature regime in which the electrical resistivity of this system exceeds the Mott-Ioffe-Regel limit and increases linearly with temperature - a sign that there are no long-lived charged quasiparticles - although the phonons remain well-defined quasiparticles.
• The long-lived phonons determine $\lambda_L$, rendering it parametrically smaller than the theoretical upper-bound $\lambda_L \ll \lambda_{max}=2\pi T/\hbar$.
• Significantly, the chaos properties seem to be intrinsic - $\lambda_L$ and $v_B$ are the same for electronic and phononic operators.