Charge and spin current statistics of the open Hubbard model with weak coupling to the environment

Based on generalization and extension of our previous work [Phys. Rev. Lett. 112, 067201 (2014)] to multiple independent Markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. Only the next-to-leading and higher orders depend on the Hubbard interaction parameter. The physical results are related to those for the $XXZ$ model in the analogous setup implying a certain universality, which potentially holds in this class of nonequilibrium models.

Figure 1

The first five (a) charge and (b) spin current cumulants for ${\mu }_1={\mu }_2=1/3$ at weak system-bath coupling $\varepsilon =0.05$ and intermediate interaction strength $u=2$. Note that the choice of ${\mu }_1={\mu }_2$ corresponds physically to the Lindblad jump operators taking in and putting out the same number of spin-up and spin-down fermions on average, which is reflected in the fact that the odd cumulants are zero in (b). The red (dashed) lines are the first-order corrections and the blue (full) ones are the third-order ones.