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Directly in the thermodynamic limit, we show how to combine imaginary andreal time evolution of tensor networks to efficiently and accurately find thenonequilibrium steady states (NESS) of one-dimensional dissipative quantumlattices governed by the Lindblad master equation. The imaginary time evolutionfirst bypasses any highly correlated portions of the real-time evolutiontrajectory by directly converging to the weakly correlated subspace of theNESS, after which real time evolution completes the convergence to the NESSwith high accuracy. We demonstrate the power of the method with the dissipativetransverse field quantum Ising chain. We show that a crossover of an orderparameter shown to be smooth in previous finite-size studies remains smooth inthe thermodynamic limit.

Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution