We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids, to fast scramblers. The analytic calculation, controlled by a small coupling constant and large $N$ , allows us to clarify the relations between the quasiparticle relaxation rate $1/\ensuremath{\tau}$ and the Lyapunov exponent ${\ensuremath{\lambda}}_{L}$ characterizing scrambling. In the Fermi liquid states we find that the quasiparticle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where $1/\ensuremath{\tau}\ensuremath{\gg}T$, we find that ${\ensuremath{\lambda}}_{L}$ is always $T$ linear with a prefactor that is independent of the coupling constant in the limit of weak coupling. Instead it is determined by a scaling exponent that characterizes the relaxation rate. ${\ensuremath{\lambda}}_{L}$ approaches the general upper bound $2\ensuremath{\pi}T$ at the transition to a fast scrambling state. Finally, in a marginal Fermi liquid state the exponent is linear in temperature with a prefactor that vanishes as a nonanalytic function $\ensuremath{\sim}gln(1/g)$ of the coupling constant $g$ .We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids, to fast scramblers. The analytic calculation, controlled by a small coupling constant and large $N$, allows us to clarify the relations between the quasiparticle relaxation rate $1/\ensuremath{\tau}$ and the Lyapunov exponent ${\ensuremath{\lambda}}_{L}$ characterizing scrambling. In the Fermi liquid states we find that the quasiparticle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where $1/\ensuremath{\tau}\ensuremath{\gg}T$, we find that ${\ensuremath{\lambda}}_{L}$ is always $T$ linear with a prefactor that is independent of the coupling constant in the limit of weak coupling. Instead it is determined by a scaling exponent that characterizes the relaxation rate. ${\ensuremath{\lambda}}_{L}$ approaches the general upper bound $2\ensuremath{\pi}T$ at the transition to a fast scrambling state. Finally, in a marginal Fermi liquid state the exponent is linear in temperature with a prefactor that vanishes as a nonanalytic function $\ensuremath{\sim}gln(1/g)$ of the coupling constant $g$.

arXiv:2006.02485Physical review. B./Physical review. BAug 18, 202023 citations

Odd relaxation in three-dimensional Fermi liquids

Seth Musser, S. Das Sarma, Johannes Hofmann

Recent theoretical works predict a hierarchy of long-lived, nonhydrodynamic modes in two-dimensional Fermi liquids arising from the feature—supposedly unique to two dimensions—that relaxation by head-on scattering is not efficient in the presence of Pauli blocking. This leads to a parity-based separation of scattering rates, with odd-parity modes relaxing much more slowly than even-parity ones. In this work, we establish that a similar effect exists in isotropic three-dimensional (3D) Fermi liquids, even though relaxation does not proceed solely by head-on scattering. We show that while the relaxation rates of even and odd modes in 3D share the same leading-order ∼ T 2 low-temperature scaling typical of Fermi liquids, their magnitudes differ, with odd-parity modes relaxing more slowly than even ones for a broad class of interactions. We find a relative difference between odd-parity and even-parity relaxation rates as large as 40 % just by Pauli blocking alone, with a strong additional dependence on the scattering potential, such that the odd-even staggering is further enhanced by interactions that favor large-angle scattering. We identify signatures of these odd-parity relaxation rates in the static transverse conductivity as well as the transverse collective mode structure. Our results establish the unexpected existence of a tomographiclike regime in higher-dimensional Fermi liquids and suggest experimental probes via transport measurements.Recent theoretical works predict a hierarchy of long-lived, nonhydrodynamic modes in two-dimensional Fermi liquids arising from the feature—supposedly unique to two dimensions—that relaxation by head-on scattering is not efficient in the presence of Pauli blocking. This leads to a parity-based separation of scattering rates, with odd-parity modes relaxing much more slowly than even-parity ones. In this work, we establish that a similar effect exists in isotropic three-dimensional (3D) Fermi liquids, even though relaxation does not proceed solely by head-on scattering. We show that while the relaxation rates of even and odd modes in 3D share the same leading-order ∼ T 2 low-temperature scaling typical of Fermi liquids, their magnitudes differ, with odd-parity modes relaxing more slowly than even ones for a broad class of interactions. We find a relative difference between odd-parity and even-parity relaxation rates as large as 40 % just by Pauli blocking alone, with a strong additional dependence on the scattering potential, such that the odd-even staggering is further enhanced by interactions that favor large-angle scattering. We identify signatures of these odd-parity relaxation rates in the static transverse conductivity as well as the transverse collective mode structure. Our results establish the unexpected existence of a tomographiclike regime in higher-dimensional Fermi liquids and suggest experimental probes via transport measurements.

arXiv:2508.18342Physical Review ResearchJan 16, 20261 citation

N

, allows us to clarify the relations between the quasiparticle relaxation rate $1/\ensuremath{\tau}$ and the Lyapunov exponent ${\ensuremath{\lambda}}_{L}$ characterizing scrambling. In the Fermi liquid states we find that the quasiparticle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where $1/\ensuremath{\tau}\ensuremath{\gg}T$, we find that ${\ensuremath{\lambda}}_{L}$ is always

T

linear with a prefactor that is independent of the coupling constant in the limit of weak coupling. Instead it is determined by a scaling exponent that characterizes the relaxation rate. ${\ensuremath{\lambda}}_{L}$ approaches the general upper bound $2\ensuremath{\pi}T$ at the transition to a fast scrambling state. Finally, in a marginal Fermi liquid state the exponent is linear in temperature with a prefactor that vanishes as a nonanalytic function $\ensuremath{\sim}gln(1/g)$ of the coupling constant

g