Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution
Adil A. Gangat1*, Te I1, Ying-Jer Kao1,2
1Department of Physics, National Taiwan University, Taipei, Taiwan
2National Center of Theoretical Sciences, National Tsinghua University, Hsinchu, Taiwan
* presenting author:Adil Gangat,
Directly in the thermodynamic limit, we show how to combine imaginary and real time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESS) of one-dimensional dissipative quantum lattices governed by the Lindblad master equation. This is achieved by directly exploiting exponential decay of two-point correlators in the NESS. The imaginary time evolution first bypasses any highly correlated portions of the real-time evolution trajectory by directly converging to the weakly correlated subspace of the NESS, after which real time evolution completes the convergence to the NESS with high accuracy. We demonstrate the power of the method with the dissipative transverse field quantum Ising chain. We show that a smooth crossover of an order parameter shown in previous finite-size studies remains smooth in the thermodynamic limit.

Keywords: tensor networks, non-equilibrium, Ising, dissipation, matrix product state