{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0df495ade77d5d55e31b32ae4427e943d54eb40cf623e39d1c0fcc696b1159e8","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"49cbde5f6d0656d3c0a90307ca22f680c5a2eed0b1f514f31ae991ec472e71d7","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.frustrated-heisenberg.square-j1j2-intermediate","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"On the square lattice, a second-neighbor coupling competes with the nearest-neighbor one and destroys magnetic order over a window of ratios. What replaces it, a spin liquid, a pattern of spin singlets or both in sequence, has been debated for decades.","posed_since":"1988","precise":"H = J1 sum_<ij> S_i . S_j + J2 sum_<<ij>> S_i . S_j, $S = 1/2$, square lattice, roughly $0.45 < J2/J1 < 0.62$. Determine the phases between Neel and stripe order (gapless spin liquid, plaquette or columnar VBS, or a sequence) with boundaries and the nature of each transition. An answer is the phase diagram with extrapolated order parameters and gaps.","problem_ref":null,"references":"","settled_by":"Agreement among DMRG, PEPS, neural-network and variational Monte Carlo on the extrapolated VBS order and spin gap across the window.","status_note":"DMRG finds a narrow possible spin liquid between Neel order and a plaquette VBS (Gong et al., PRL 2014), and 2024 DMRG confirms plaquette rather than columnar VBS order (arXiv:2406.17417); a 2025 cluster-embedding study instead finds plaquette and columnar VBS phases split at $J2/J1 = 0.55$ with no spin liquid (arXiv:2511.06423).","title":"Intermediate phase of the square-lattice $J1-J2$ Heisenberg 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