Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model

[2505.23728] Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Disordered Systems and Neural Networks arXiv:2505.23728 (cond-mat) [Submitted on 29 May 2025 ( v1 ), last revised 19 Jun 2026 (this version, v3)] Title: Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model Authors: Ojasvi Sharma , Sandipan Manna , Prashant Shekhar Rao , G J Sreejith View a PDF of the paper titled Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model, by Ojasvi Sharma and 3 other authors View PDF HTML (experimental) Abstract: We obtain the $\rm{p4m}$-symmetric Group Convolutional Neural Network (GCNN) representations of the lowest energy eigenstate of the quantum dimer model on $L{\times} L$ square-lattice in each of the ${(L^2+18L+72)}/{8}$ irreducible representations (irreps) of the lattice space group and use these to investigate the competition between columnar, plaquette and mixed phases. The networks are optimized within each irrep by minimizing the energy, which is estimated from samples obtained via an efficient directed loop sampler. In extensive benchmarks, we show excellent agreement in energy estimates, order parameters and correlation functions with exact diagonalization or quantum Monte Carlo in systems of sizes $8\leq L\leq 32$. Analysis of the scaling of the gaps in different representation sectors with systems of sizes up to $L=32$ suggest a $4$-fold degenerate ground state for $V\leq 0.4$ narrowing the regime of possible mixed/plaquette phases to $0.4 < V< 1$. Our results show that GCNN is a powerful tool to investigate ground state phase diagrams. The approach paves the way for even more accurate results by producing highly accurate variational baseline wavefunctions for quantum Monte Carlo approaches. Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn) ; Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2505.23728 [cond-mat.dis-nn] (or arXiv:2505.23728v3 [cond-mat.dis-nn] for this version) https://doi.org/10.48550/arXiv.2505.23728 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. B 114, 014408 (2026) Related DOI : https://doi.org/10.1103/nvcg-mb1r Focus to learn more DOI(s) linking to related resources Submission history From: G J Sreejith [ view email ] [v1] Thu, 29 May 2025 17:56:01 UTC (2,153 KB) [v2] Thu, 9 Apr 2026 12:22:14 UTC (3,791 KB) [v3] Fri, 19 Jun 2026 12:56:07 UTC (6,692 KB) Full-text links: Access Paper: View a PDF of the paper titled Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model, by Ojasvi Sharma and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.dis-nn < prev | next > new | recent | 2025-05 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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