Dynamics and Charge Fluctuations in Large-q Sachdev-Ye-Kitaev Lattices

Abstract

It is known that the large-$q$ complex Sachdev-Ye-Kitaev (SYK) dot thermalizes instantaneously under rather general dynamical protocols. We consider a lattice of such dots coupled together, allowing for $r/2$ body hopping of particles between nearest neighbors. We develop a rather general analytical framework to study the dynamics to leading order in $1/q$ on such a lattice, allowing for arbitrary time dependent couplings, hence general dynamical protocols. We find that the physics of the diffusive case $r>2$ is effectively the same as the kinetic case $r=2$, assuming $r=\mathcal{O}(q^0)$. Remarkably, we find that the local charge densities ${\mathcal{Q}}_i$ form a closed set of equations. They however only show fluctuations of the order $\mathcal{O}({\mathcal{Q}}_i/q)$, hence remaining constant in the limit $q\to \infty$. Despite this effective lack of charge dynamics, the dots do not in fact behave as isolated lattice sites which would thermalize instantaneously. Indeed, we show via a proof by contradiction that such instantaneously thermalize is not generally possible for a connected lattice. Importantly, the results are shown to be independent of the dimensionality of the lattice.

Same as published version with two minor typo corrections in Eqs. (4) and (8), 15 pages, 1 figure

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Cited by in corpus (3)

• Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit
• Thermodynamics and dynamics of coupled complex SYK models
• Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study