Open Quantum System Dynamics from Infinite Tensor Network Contraction

Abstract

Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of a tensor network. We show that for Gaussian environments highly efficient contraction to matrix product operator (MPO) form can be achieved with infinite MPO evolution methods, leading to significant computational speed-up over existing proposals. The result structurally resembles open system evolution with carefully designed auxiliary degrees of freedom, as in hierarchical or pseudomode methods. Here, however, these degrees of freedom are generated automatically by the MPO evolution algorithm. Moreover, the semi-group form of the resulting propagator enables us to explore steady-state physics, such as phase transitions.

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• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
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• Tree-like process tensor contraction for automated compression of environments
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• Path Integral Formalism for Quantum Open Systems
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• Verifying Quantum Memory in the Dynamics of Spin Boson Models
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• Extracting Coupling-Mode Spectral Densities with Two-Dimensional Electronic Spectroscopy
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• Process Tensor Approaches to Non-Markovian Quantum Dynamics
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• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
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