aiqbench analysis
This research investigates thermalization dynamics in large-$q$ SYK models, revealing that while causal Green's functions exhibit instantaneous thermal behavior, off-diagonal correlations remain inherently non-thermal. The study corrects previous conjectures regarding divergent thermalization rates, demonstrating instead a decaying rate proportional to $T q^{-1}$ when accounting for all correlation blocks. These findings refine the theoretical understanding of Planckian dynamics in strongly correlated quantum systems relevant to quantum simulation and condensed matter theory.
What does "instant thermalization" in large-$q$ SYK models mean?
arXiv:2609.17794v1 Announce Type: cross Abstract: Motivated by the Planckian thermalization rate $\Gamma \sim T$ observed in the two-body interacting SYK model, we study thermalization in the $q/2$-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in $1/q$. It was conjectured that the thermalization may still be Planckian but with a divergent rate $\Gamma \sim T q$, explaining the ``instantaneous'' part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time $t = 0$ and indeed find a Planckian rate, albeit with the unexpected decaying behavior $\Gamma \sim T q^{-1} $. This is contrasted with the behavior of the causal Green's function $\mathcal{G}(t_1, t_2)$, which instantly acquires a thermal form in the two-time plane block $t_1, t_2 > 0$. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks $t_1 \cdot t_2 < 0$ are inherently non-thermal at any $q$. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.
Abstract:Motivated by the Planckian thermalization rate $\Gamma \sim T$ observed in the two-body interacting SYK model, we study thermalization in the $q/2$-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in $1/q$. It was conjectured that the thermalization may still be Planckian but with a divergent rate $\Gamma \sim T q$, explaining the ``instantaneous'' part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time $t = 0$ and indeed find a Planckian rate, albeit with the unexpected decaying behavior $\Gamma \sim T q^{-1} $. This is contrasted with the behavior of the causal Green's function $\mathcal{G}(t_1, t_2)$, which instantly acquires a thermal form in the two-time plane block $t_1, t_2 > 0$. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks $t_1 \cdot t_2 < 0$ are inherently non-thermal at any $q$. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.
Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)
arXiv:2609.17794 [cond-mat.str-el]
(or arXiv:2609.17794v1 [cond-mat.str-el] for this version)
https://doi.org/10.48550/arXiv.2609.17794 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 220 words
