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.

Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space

“…The MPS formulation is an extremely powerful and versatile tool to study quantum many-body physics, in particular for one-dimensional systems with low or moderate entanglements. 55, MPS has also been applied to open quantum system dynamics, in particular in connection with other approaches based on a reduced system dynamics description, such as quasi-adiabatic path-integral approach, [66][67][68] and hierarchy of pure state. 69,70 The MPS representation, as a wave function approach, can be considered as a special case of the multi-layer multiconfigurational time-dependent Hartree (ML-MCTDH) method, 33,[71][72][73][74][75] which has also been applied to a variety of prototype open quantum systems.…”