A Pairwise Connected Tensor Network Representation of Path Integrals

Abstract

It has been recently shown how the tensorial nature of real-time path integrals involving the Feynman-Vernon influence functional can be utilized using matrix product states, taking advantage of the finite length of the non-Markovian memory. Tensor networks promise to provide a new, unified language to express the structure of path integral. Here, a generalized tensor network is derived and implemented specifically incorporating the pairwise interaction structure of the influence functional, allowing for a compact representation and efficient evaluation. This pairwise connected tensor network path integral (PCTNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage requirements and performance are compared with iterative quasi-adiabatic propagator path integral and iterative blip-summed path integral. Finally, the viability of using PCTNPI for simulating multistate problems is demonstrated taking advantage of the compressed representation.

arXiv comment10 pages, 13 figures

References in corpus (12)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Real time evolution using the density matrix renormalization group
• Entanglement renormalization
• A class of quantum many-body states that can be efficiently simulated
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) Approach to the Correlated Exciton-Vibrational Dynamics in the FMO Complex
• Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems
• Quantum simulation of the spin-boson model with a microwave circuit
• A Multisite Decomposition of the Tensor Network Path Integrals
• Tensor network based machine learning of non-Markovian quantum processes

Cited by in corpus (4)

• Real time evolution of Anderson impurity models via tensor network influence functionals
• A Multisite Decomposition of the Tensor Network Path Integrals
• Tensor Network Path Integral Study of Dynamics in B850 LH2 Ring with Atomistically Derived Vibrations
• Zero-Cost Corrections to Influence Functional Coefficients from Bath Response Functions