{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"00dde1e88828c2cdeccbeafd7555115b6c7c056848e96324103b5389bd86cbf1","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"8c6f5902577f0e60b5dd8e50ca86ceb09a7849304b395d70acae944679857263","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.frustrated-heisenberg.er2ti2o7-selection","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Er2Ti2O7 orders into one particular spin pattern although its main interactions treat a whole continuous family equally. Both quantum fluctuations and virtual excitations to higher atomic energy levels can pick that pattern, and their relative share is unsettled.","posed_since":"2012","precise":"For Er2Ti2O7 with anisotropic nearest-neighbor exchange $(J_{zz}, J_{pm}, J_{pmpm}, J_{zpm})$ fitted to neutron data, compute the energy splitting between the $\\psi_2$ and $\\psi_3$ states and the pseudo-Goldstone gap produced by (a) quantum zero-point fluctuations within the ground doublet and (b) virtual crystal-field excitations, and compare with the measured gap. An answer gives the fraction of the measured gap due to each mechanism.","problem_ref":null,"references":"","settled_by":"A calculation including both spin-wave zero-point energy and second-order crystal-field corrections, with exchange fitted to the full neutron spectrum, compared with the measured gap.","status_note":"A pseudo-Goldstone gap was observed (Ross et al., PRL 2014) as order by disorder predicts; Rau et al. (PRL 2016) showed virtual crystal-field fluctuations give a comparable selection.","title":"Quantum order by disorder or virtual crystal-field selection in 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