Lindblad driving for nonequilibrium steady-state transport for noninteracting quantum impurity models

Frauke Schwarz

Frauke Schwarz, Jan von Delft, Andreas Weichselbaum

Frauke Schwarz, Moshe Goldstein, Antonius Dorda +3 more

The description of interacting quantum impurity models in steady-state nonequilibrium is an open challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing a truly open quantum system are seemingly incompatible. One possibility to bridge this gap is the use of Lindblad-driven discretized leads (LDDL): one couples auxiliary continuous reservoirs to the discretized lead levels and represents these additional reservoirs by Lindblad terms in the Liouville equation. For quadratic models governed by Lindbladian dynamics, we present an elementary approach for obtaining correlation functions analytically. In a second part, we use this approach to explicitly discuss the conditions under which the continuum limit of the LDDL approach recovers the correct representation of thermal reservoirs. As an analytically solvable example, the nonequilibrium resonant level model is studied in greater detail. Lastly, we present ideas towards a numerical evaluation of the suggested Lindblad equation for interacting impurities based on matrix product states. In particular, we present a reformulation of the Lindblad equation, which has the useful property that the leads can be mapped onto a chain where both the Hamiltonian dynamics and the Lindblad driving are local at the same time. Moreover, we discuss the possibility to combine the Lindblad approach with a logarithmic discretization needed for the exploration of exponentially small energy scales.

Matan Lotem, Andreas Weichselbaum, Jan von Delft +1 more

This work introduces a tensor-network algorithm for nonequilibrium quantum impurities coupled to finite leads which in turn are weakly coupled to Lindblad reservoirs, to allow for a nonequilibrium steady state while capturing many-body correlations as in the equilibrium numerical renormalization group

Yi Liu, Zixuan Hu, Xiao Zheng +1 more

We propose a quantum algorithm that solves the electron transport problem over a molecular junction via the variational quantum eigensolver (VQE) method. We regard the molecular junction as an impurity model coupled with discrete Lindblad dissipaters. The problem of solving for the nonequilibrium steady state (NESS) of the electron transport is converted to a variational optimization problem for finding the zero eigenstates of non-Hermitian Liouville superoperators (Liouvillian). With a modified Jordan-Wigner transformation, the variational kernel of the Hermitian product of fermionic Liouville superoperators would be mapped as the cost function on the quantum circuit, and the corresponding density matrix of the NESS can be found by the VQE process. We demonstrate this approach on a single-level molecular model and estimate the $I\text{\ensuremath{-}}V$ curve, verifying the accuracy of this algorithm.