Uniform process tensor approach for the calculation of multi-time correlation functions of non-Markovian open systems

Abstract

The process tensor framework to open quantum systems provides the most general description of multi-time correlations in non-Markovian quantum dynamics. A compressed representation of a process tensor in terms of matrix product operators (MPO) can be used for numerically exact calculations of multi-time correlation functions in systems strongly coupled to a non-Markovian reservoir. We show here that the numerical scaling for computing multi-dimensional spectra can be significantly improved using a time-translation invariant MPO representation of the process tensor obtained from the uniform time-evolving matrix product operator (uniTEMPO) method. In particular, this approach provides a spectral representation of the non-Markovian dynamics that gives direct access to correlation functions in Fourier-space, avoiding explicit real-time evolution. We calculate linear and 2D electronic spectra for an example system and discuss the performance and numerical scaling of our simulations.

References in corpus (33)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Hierarchy of stochastic pure states for open quantum system dynamics
• Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories
• Matrix Product States for dynamical simulation of infinite chains
• Efficient simulation of finite-temperature open quantum systems
• Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
• Numerically exact open quantum systems simulations for arbitrary environments using automated compression of environments
• Influence matrix approach to many-body Floquet dynamics
• Optimized auxiliary oscillators for the simulation of general open quantum systems
• Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems
• Exact dynamics of non-additive environments in non-Markovian open quantum systems
• Real time evolution of Anderson impurity models via tensor network influence functionals
• Non-Markovian quantum state diffusion for absorption spectra of molecular aggregates
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Using the Environment to Understand non-Markovian Open Quantum Systems
• Open Quantum System Dynamics from Infinite Tensor Network Contraction
• Tensor network simulation of chains of non-Markovian open quantum systems
• Linear, third- and fifth-order nonlinear spectroscopy of a charge transfer system coupled to an underdamped vibration
• Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models
• Higher-order photon correlation as a tool to study exciton dynamics in quasi-2D nanoplatelets
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion
• Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model
• Process tensor approaches to modeling two-dimensional spectroscopy
• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Semi-group influence matrices for non-equilibrium quantum impurity models
• Steady-state dynamical mean field theory based on influence functional matrix product states
• Two-dimensional spectroscopy of Rydberg gases
• Capturing long-range memory structures with tree-geometry process tensors
• Exact Floquet dynamics of strongly damped driven quantum systems
• Verifying Quantum Memory in the Dynamics of Spin Boson Models
• A Markovian approach to $N$-photon correlations beyond the quantum regression theorem