Universal quench dynamics of lattice $q$ fermion Yukawa Sachdev-Ye-Kitaev model

TL;DR

The paper investigates non-Fermi liquid quench dynamics in a lattice Yukawa-SYK model with $q$ fermions and one boson, using disorder-averaged large-$N$ dynamical mean-field theory and real-time Kadanoff-Baym equations. It analyzes quenches that fix the Yukawa coupling $g$ while varying the lattice coupling $v$, revealing universal Planckian relaxation characterized by two separate temperatures for bosons and fermions and relaxation rates that scale linearly with the final temperature $T_f$. The authors compute time-resolved spectral functions, distribution functions, and effective temperatures, showing robust two-temperature dynamics and a linear $T_f$ dependence across $q=2,4,6$ and various $g$, with fermions and bosons relaxing at distinct rates. These results provide a microscopic route to Planckian transport in non-quasiparticle systems and connect to experimental topics on strange metals and light-driven unconventional superconductivity.

Abstract

We study the quantum quench of the Yukawa Sachdev-Ye-Kitaev model and one of its lattice extensions with $q$ fermions and one boson. Several equilibrium properties are computed for general $q$ with different parameter scaling within the large-$N$ dynamical mean field scheme. The non-Fermi liquid quench dynamics are studied by integrating the Kadanoff-Baym equations for switching off the lattice term with constant Yukawa coupling or quenching to different final Yukawa couplings. The post-quench oscillations and relaxation dynamics are insensitive to the quench amplitudes deep inside the non-Fermi liquid phase. With weak lattice coupling quenches, we find universal thermalization dynamics similar to the SYK model; however, with two temperatures and two distinct relaxation rates for bosons and fermions, both signal Planckian relaxations without quasiparticles, as in strange metals.

Figures (16)

• Figure 1: The half-filling phase diagram for $q=2$ according to the reference Valentinis2023 using the equations provided there. (a) $v=0$. The two crossovers separate three phases: the free fermion phase, the non-Fermi liquid phase (SYK-NFL), and the impurity-like non-Fermi liquid phase (Impurity-NFL). (b) $v=0.1$. The Fermi liquid phase (SYK-FL) is marked blue. (c) $v=1$. The SYK-FL phase is larger than $v=0.1$. The red cross marks the typical pre-quench setting, $\beta=40$, $g=1$.
• Figure 2: Imaginary time Green's functions, (a) for fermion and (b) for boson. Solid lines are numerics and dashed lines are conformal solutions with the scaling dimensions in Table \ref{['tab:exponent_table1']}. Here $\beta=160\omega_0^{-1}$, $g^2=\omega_0^3 2^{q-1}/q$, $\lambda=4/q^2$ and $v=0$. One can see the computed $q$ dependent exponents fit well. Note for reaching low temperature, we used $10^4$ Matsubara frequencies. One expects the agreement when $\frac{\pi}{\beta \sin(\pi \tau/\beta)}$ is small.
• Figure 3: Spectral functions (a) for fermions and (c) for bosons. Effective distributions (b) for fermions and (d) for bosons. Here we fixed $g=1$, $q=2$ with quench protocol $v_i=0.1$, $v_f=0$. We use $\beta=40$ here. The insets of (c) and (d) are zoomed-in pictures. The spectral function changes mainly in the low-frequency region for this small quench. The distribution functions have smooth time dependence and can give well-defined effective temperatures that can be extracted from the slopes of effective distributions around $\omega=0$ and be used for the analysis of temperature dynamics. Here, the $\beta_i$ is the initial temperature, and the $\beta_f$ is the fit temperature at the latest time. One can see that the initial and final distributions match the expected equilibrium distribution.
• Figure 4: Time dependences of boson occupations $n^{(b)}(t)$, boson correlation energies $|E^{(b)}_{\mathrm{corr}}(t)|$ and boson renormalized frequencies $\omega_{\mathrm{r}}^2(t_{\mathrm{a}})$. The protocol is $v_i$ to $v_f=0$ with fixed $g=1$, $q=2$. The lower right figure shows the log-log plot for $v_i=0.1$ of those three quantities, and the agreement of their time dependence can be directly observed. For $n^{(b)}(t)$ and $|E^{(b)}_{\mathrm{corr}}(t)|$, one can see that they stay constant before the quench at $t=0$. The precursors of the $\omega_{\mathrm{r}}$ before the quenches are because of using the center of mass slices two-point functions, which can contain the post-quenched part even when $t_{\mathrm{a}}<0$. We find damping oscillation dynamics are different from the temperature dynamics.
• Figure 5: Center of the mass time dependence of effective inverse temperature and temperature. We fixed $g=1$, $q=2$. The crosses are for fermions and circles for bosons. Note here we use strong quenches $v_i=0.1,0.2,0.3,0.4,0.5$ to give a broader view of the quench parameter region. The data shown is sparse for visibility. From (a), we can see precursors of the effective inverse temperatures decaying. This is because the center of mass, i.e., Wigner coordinate, two-point function, is used for temperature extraction, which means even for $t_{\mathrm{a}}<0$, there can be post-quenched effects. For $t_{\mathrm{a}}>0$, the two-point functions are purely post-quenched. The effective temperatures are shown in (b). We can see that the bosons and fermions have different relaxation rates, and the quench affects the different subsystems differently.