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arXiv · 2601.17718

Tree tensor network impurity solver based on Cayley-tree mapping

Bo Zhan·Jia-Lin Chen·Zhen Fan·Tao Xiang
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Abstract

We introduce a tree tensor network (TTN) impurity solver that enables highly efficient and accurate real-time simulations of quantum impurity models. By decomposing a noninteracting bath Hamiltonian into a Cayley tree, the method provides a tensor network representation that naturally captures the multiscale entanglement structure intrinsic to impurity-bath systems. This geometry differs from conventional chain-based mappings and yields a substantial reduction of entanglement, allowing accurate ground-state properties and long-time dynamics to be captured at significantly lower bond dimensions. Benchmark calculations for the single-impurity Anderson model demonstrate that the TTN solver achieves markedly enhanced resolution of real-frequency spectral functions, without invoking analytic continuation. This impurity solver provides a balanced, scale-uniform description of impurity physics and offers a versatile approach for real-time dynamical mean-field theory and related applications involving quantum impurity models.

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Bo Zhan, Jia-Lin Chen, Zhen Fan, Tao Xiang. 2026-01-25. Tree tensor network impurity solver based on Cayley-tree mapping. https://doi.org/10.1103/ycty-d5f9

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