{"paper":{"title":"Gapped and gapless phases of frustration-free spin-1/2 chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"David Gosset, Sergey Bravyi","submitted_at":"2015-03-13T12:24:33Z","abstract_excerpt":"We consider a family of translation-invariant quantum spin chains with nearest-neighbor interactions and derive necessary and sufficient conditions for these systems to be gapped in the thermodynamic limit. More precisely, let $\\psi$ be an arbitrary two-qubit state. We consider a chain of $n$ qubits with open boundary conditions and Hamiltonian $H_n(\\psi)$ which is defined as the sum of rank-1 projectors onto $\\psi$ applied to consecutive pairs of qubits. We show that the spectral gap of $H_n(\\psi)$ is upper bounded by $1/(n-1)$ if the eigenvalues of a certain two-by-two matrix simply related "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04035","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"}