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arXiv · 2106.14934

A Pairwise Connected Tensor Network Representation of Path Integrals

Amartya Bose
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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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Amartya Bose. 2021-07-06. A Pairwise Connected Tensor Network Representation of Path Integrals. https://doi.org/10.1103/physrevb.105.024309

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