Nonequilibrium steady state of quantum impurities: A numerically-exact tensor-network approach

The accurate description of the nonequilibrium steady state properties of qubits coupled to different environments, or ``quantum impurities’’ (such as an interacting quantum dot, e.g., in the Kondo regime, under the application of a finite bias voltage) is a central open problem in condensed matter physics. In order to study such systems, we employ a novel approach where the impurity is coupled to a finite number of lead levels, which in turn are incoherently coupled to baths, resulting in a Lindblad master equation for the density operator of an effective 1D system describing the impurity and the finite leads. Numerically exact tensor-networks based methods are employed in order to target the Lindblad equation steady state. First, equilibrium NRG is used to find the relevant Hilbert subspace of the impurity and its vicinity. The full system is then evolved towards the steady state using a time dependent Matrix Product Density Operator algorithm. Our results show that the Lindblad dissipation, if appropriately tuned, can cut off the entanglement entropy growth, which otherwise is the limiting factor in tensor-networks methods, while at the same time giving rise to the correct infinite system steady state observables.