Exact and fast series expansions for quantum models with long-range interactions
Abstract
Over the past decade, high-order series expansions based on linked-cluster methods have become an important tool for studying low-energy properties of gapped quantum systems with long-range interactions. We introduce a deterministic framework that removes a central computational bottleneck of this method. Our graph zeta method replaces the costly and statistically noisy Monte Carlo (MC) evaluation of high-dimensional lattice sums by a systematic, high-precision computation that delivers series coefficients within minutes on standard desktop hardware. The full momentum-dependent series is obtained in a single calculation, enabling high-resolution excitation spectra throughout the Brillouin zone. Building on the companion paper [1], the method reformulates graph-embedding sums as graph zeta functions and decomposes them into blocks classified by their treewidth tw. Low-treewidth blocks (tw≤2) admit closed expressions based on Epstein zeta functions, while higher-treewidth blocks (tw>2) are evaluated using tensor-network bucket elimination. We benchmark the approach for transverse-field Ising models with power-law interactions in 1d, 2d, and 3d, reproducing previous MC results at a fraction of the computational cost while enabling substantially denser parameter sampling. An open-source implementation makes the method directly applicable to general interactions and large parameter scans. As an application, we compare microscopic interaction models for the stacked quasi-2d transverse-field Ising triangular-lattice antiferromagnet KTmSe2 and find that a model including dipolar interactions best describes existing experimental data. The graph zeta method thus turns high-order linked-cluster expansions into a practical and deterministic tool for fast quantitative momentum-resolved modeling of short- and long-range quantum matter.
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BibTeX
@misc{duft2026exact,
title = {{Exact and fast series expansions for quantum models with long-range interactions}},
author = {Antonia Duft and Patrick Adelhardt and Jan Alexander Koziol and Andreas A. Buchheit and Kai Phillip Schmidt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.18761},
eprint = {2609.18761},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18761},
}
RIS
TY - UNPB
TI - Exact and fast series expansions for quantum models with long-range interactions
AU - Antonia Duft
AU - Patrick Adelhardt
AU - Jan Alexander Koziol
AU - Andreas A. Buchheit
AU - Kai Phillip Schmidt
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.18761
UR - https://arxiv.org/abs/2609.18761
AB - Over the past decade, high-order series expansions based on linked-cluster methods have become an important tool for studying low-energy properties of gapped quantum systems with long-range interactions. We introduce a deterministic framework that removes a central computational bottleneck of this method. Our graph zeta method replaces the costly and statistically noisy Monte Carlo (MC) evaluation of high-dimensional lattice sums by a systematic, high-precision computation that delivers series coefficients within minutes on standard desktop hardware. The full momentum-dependent series is obtained in a single calculation, enabling high-resolution excitation spectra throughout the Brillouin zone. Building on the companion paper [1], the method reformulates graph-embedding sums as graph zeta functions and decomposes them into blocks classified by their treewidth tw. Low-treewidth blocks (tw≤2) admit closed expressions based on Epstein zeta functions, while higher-treewidth blocks (tw>2) are evaluated using tensor-network bucket elimination. We benchmark the approach for transverse-field Ising models with power-law interactions in 1d, 2d, and 3d, reproducing previous MC results at a fraction of the computational cost while enabling substantially denser parameter sampling. An open-source implementation makes the method directly applicable to general interactions and large parameter scans. As an application, we compare microscopic interaction models for the stacked quasi-2d transverse-field Ising triangular-lattice antiferromagnet KTmSe_2 and find that a model including dipolar interactions best describes existing experimental data. The graph zeta method thus turns high-order linked-cluster expansions into a practical and deterministic tool for fast quantitative momentum-resolved modeling of short- and long-range quantum matter.
ER -