Higher-dimensional persistence of charge-spin competition

Determine whether the competition between charge and spin energy scales, and the associated transport behavior identified in the one-dimensional boundary-driven Fermi-Hubbard chain, persists in higher-dimensional lattices where spin and charge degrees of freedom are not separated in the same manner.

Background

The one-dimensional study attributes the observed transport resonances and dephasing-assisted enhancement regimes to distinct charge and spin energy scales near half filling: the interaction scale $U$ and the superexchange scale $J_{\mathrm{ex}}$.

The authors note that higher-dimensional systems may not exhibit the same separation of spin and charge degrees of freedom. Consequently, it is unresolved whether an analogous competition survives in higher dimensions and what form its transport signatures would take.