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arXiv · 2101.03935

Generating Function for Tensor Network Diagrammatic Summation

Wei-Lin Tu·Huan-Kuang Wu·Norbert Schuch·Naoki Kawashima·Ji-Yao Chen
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Abstract

The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the intricate summation over an extensive number of tensor diagrams. Here, we introduce a set of generating functions, which encode the diagrammatic summations as leading order series expansion coefficients. Combined with automatic differentiation, the generating function allows us to solve the problem of TN diagrammatic summation. We illustrate this scheme by computing variational excited states and dynamical structure factor of a quantum spin chain, and further investigating entanglement properties of excited states. Extensions to infinite size systems and higher dimension are outlined.

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Wei-Lin Tu, Huan-Kuang Wu, Norbert Schuch, Naoki Kawashima, Ji-Yao Chen. 2021-05-28. Generating Function for Tensor Network Diagrammatic Summation. https://doi.org/10.1103/physrevb.103.205155

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