Kardar-Parisi-Zhang scaling in the Hubbard model

Abstract

We explore the Kardar-Parisi-Zhang (KPZ) scaling in the one-dimensional Hubbard model, which exhibits global $S{U}_c(2)\otimes S{U}_s(2)$ symmetry at half-filling, for the pseudo-charge and the total spin. We analyze dynamical scaling properties of high temperature charge and spin correlations and transport. At half-filling, we observe a clear KPZ scaling in both charge and spin sectors. Away from half-filling, the $S{U}_c(2)$ charge symmetry is reduced to $U_c(1)$, while the $S{U}_s(2)$ symmetry for the total spin is retained. Consequently, transport in the charge sector becomes ballistic, while KPZ scaling is preserved in the spin sector. These findings confirm the link between non-abelian symmetries and KPZ scaling in the presence of integrability. We study two settings of the model: one involving a quench from a bi-partitioned state asymptotically close to the $T=\infty$ equilibrium state of the system, and another where the system is coupled to two markovian reservoirs at the two edges of the chain.

14 pages, 18 figures

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• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/${\mathbb{Z}}_2^2$ symmetry
• Anomalous Quantum Relaxation in the Infinite Temperature Hubbard Chain
• Integral formula for the propagator of the one-dimensional Hubbard model