A Pairwise Connected Tensor Network Representation of Path Integrals

• URL: http://arxiv.org/abs/2106.14934v4
• Date: Tue, 6 Jul 2021 17:09:02 GMT
• Title: A Pairwise Connected Tensor Network Representation of Path Integrals
• Authors: Amartya Bose
• Abstract summary: It has been recently shown how the tensorial nature of real-time path integrals involving the Feynman-Vernon influence functional can be utilized. Here, a generalized tensor network is derived and implemented specifically incorporating the pairwise interaction structure of the influence functional. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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