{"paper":{"title":"A Recipe for Constructing Frustration-Free Hamiltonians with Gauge and Matter Fields in One and Two Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"Juan Pablo Ibieta Jimenez, Miguel Jorge Bernab\\'e Ferreira, Paulo Teotonio-Sobrinho, Pramod Padmanabhan","submitted_at":"2015-03-26T02:20:27Z","abstract_excerpt":"State sum constructions, such as Kuperberg's algorithm, give partition functions of physical systems, like lattice gauge theories, in various dimensions by associating local tensors or weights, to different parts of a closed triangulated manifold. Here we extend this construction by including matter fields to build partition functions in both two and three space-time dimensions. The matter fields introduces new weights to the vertices and they correspond to Potts spin configurations described by an $\\mathcal{A}$-module with an inner product. Performing this construction on a triangulated manif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07601","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}