Non-Markovian Stochastic Schrödinger Equation: Matrix Product State Approach to the Hierarchy of Pure States

Abstract

We derive a stochastic hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open quantum system at finite temperature, which is numerically exact and efficient. HOMPS is obtained from the recently developed stochastic hierarchy of pure states (HOPS) by expressing HOPS in terms of formal creation and annihilation operators. The resulting stochastic first order differential equation is then formulated in terms of matrix product states and matrix product operators. In this way the exponential complexity of HOPS can be reduced to scale polynomial with the number of particles. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.

5 pages, 3 figures

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• Simulating optical linear absorption for mesoscale molecular aggregates: an adaptive hierarchy of pure states approach
• Optimal Tree Tensor Network Operators for Tensor Network Simulations: Applications to Open Quantum Systems
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• Stable bipolarons in open quantum systems
• Non-Markovian Quantum State Diffusion for Spin Environments
• Spectral signatures of the Markovian to Non-Markovian transition in open quantum systems
• nuHOPS: A quantum trajectory method for highly excited environments in non-Markovian open quantum dynamics
• Improved Memory Truncation Scheme for Quasi-Adiabatic Propagator Path Integral via Influence Functional Renormalization
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
• Non-Markovian dynamics in nonstationary Gaussian baths: a hierarchy of pure states approach