Generating Function For Tensor Network Diagrammatic Summation

Condensed Matter > Strongly Correlated Electrons arXiv:2101.03935 (cond-mat) [Submitted on 11 Jan 2021 (v1), last revised 28 May 2021 (this version, v2)] Title:Generating Function for Tensor Network Diagrammatic Summation Authors:Wei-Lin Tu, Huan-Kuang Wu, Norbert Schuch, Naoki Kawashima, Ji-Yao Chen View a PDF of the paper titled Generating Function for Tensor Network Diagrammatic Summation, by Wei-Lin Tu and 4 other authors View PDF

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.

Comments:	v1: 6 pages, 2 figures. v2: published version
Subjects:	Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
Cite as:	arXiv:2101.03935 [cond-mat.str-el]
(or arXiv:2101.03935v2 [cond-mat.str-el] for this version)
https://doi.org/10.48550/arXiv.2101.03935 Focus to learn more arXiv-issued DOI via DataCite
Journal reference:	Phys. Rev. B 103, 205155 (2021)
Related DOI:	https://doi.org/10.1103/PhysRevB.103.205155 Focus to learn more DOI(s) linking to related resources

Submission history

From: Ji-Yao Chen [view email] [v1] Mon, 11 Jan 2021 14:55:27 UTC (207 KB) [v2] Fri, 28 May 2021 15:41:01 UTC (208 KB) Full-text links:

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