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arXiv · 2312.11705

Complex Time Evolution in Tensor Networks

M. Grundner·P. Westhoff·F. B. Kugler·O. Parcollet·U. Schollwöck
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Abstract

Real-time calculations in tensor networks are strongly limited in time by entanglement growth, restricting the achievable frequency resolution of Green's functions, spectral functions, self-energies, and other related quantities. By extending the time evolution to contours in the complex plane, entanglement growth is curtailed, enabling numerically efficient high-precision calculations of time-dependent correlators and Green's functions with detailed frequency resolution. Various approaches to time evolution in the complex plane and the required post-processing for extracting the pure real-time and frequency information are compared. We benchmark our results on the examples of the single-impurity Anderson model using matrix-product states and of the three-band Hubbard-Kanamori and Dworin-Narath models using a tree tensor network. Our findings indicate that the proposed methods are also applicable to challenging realistic calculations of materials.

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M. Grundner, P. Westhoff, F. B. Kugler, O. Parcollet, U. Schollwöck. 2023-12-18. Complex Time Evolution in Tensor Networks. https://doi.org/10.1103/physrevb.109.155124

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