{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"04e1f267276b0f29505f33d6440d3b27aef2fd0a3bac506d3abe988dff312fe9","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"32feef1c78017a1d943bbcd849e0f7b84c8293d48b45dc5711bfac1609389aa3","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.spin-chains.blbq-nematic-window","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"The spin-1 chain with both ordinary and squared spin couplings has a known phase diagram except near its boundary with ferromagnetism. There a spin-nematic phase was proposed, and numerics have not cleanly confirmed or excluded it.","posed_since":"1991","precise":"$H = \\sum_i [\\cos(\\theta) S_i . S_{i+1} + \\sin(\\theta) (S_i . S_{i+1})^2]$, $S = 1$, for $\\theta$ just above $-3\\pi/4$, next to the ferromagnetic phase. Determine whether the dimerized phase extends all the way to $\\theta = -3\\pi/4$ with an exponentially small gap, or a gapless or gapped nematic phase intervenes. An answer gives the phase boundary and the dimerization order parameter as $\\theta \\to -3\\pi/4$.","problem_ref":null,"references":"","settled_by":"High-precision DMRG or field-theory analysis that resolves the exponentially small gap and dimerization near $\\theta = -3\\pi/4$.","status_note":"Proposed by Chubukov (1991); numerics favor dimerization up to the ferromagnetic boundary but cannot resolve the exponentially small gap.","title":"Is there a nematic phase in the spin-1 bilinear-biquadratic 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