RESUMO
We investigate the many-body quantum chaos of non-Fermi liquid states with Fermi surfaces in two spatial dimensions by computing their out-of-time-order correlation functions. Using a recently proposed large N theory for the critical Fermi surface, and the ladder identity of Gu and Kitaev, we show that the chaos Lyapunov exponent takes the maximal value of 2πk_{B}T/â, where T is the absolute temperature. We also examine a phenomenological model that can be continuously tuned between a non-Fermi liquid without quasiparticles and a Fermi liquid with quasiparticles. We find that the Lyapunov exponent becomes smaller than the maximal value precisely when quasiparticles are restored.
RESUMO
We investigate a model of electrons with random and all-to-all hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev-Ye-Kitaev-like large-M limit with SU(M) spin symmetry. The saddle-point equations of this model are similar to approximate dynamic mean-field equations of realistic, nonrandom, t-J models. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non-Fermi-liquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a time-reparameterization symmetry, akin to Sachdev-Ye-Kitaev (SYK) models, which contributes a linear-in-temperature resistivity over the full range of doping where the solution is present. It is therefore an attractive mean-field description of the overdoped region of cuprates, where experiments have observed a linear-T resistivity in a broad region. The critical metal also displays a strong particle-hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a low-doping spin-glass phase and compute a critical doping value. We also describe the properties of this metallic spin-glass phase.
