{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"95acefa56d9dffc69465a5351317a86a4cc16c56442cb42151e9f8b6910b77d1","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["8e4bec8a3360c242f46e80b11623db9058d1b79a5722dda9c14f8b4592c84d53","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"a2c9aa1f3d2dd18a8fdd4a3a5f969eacf30ceae00ca5b8ce7c84bf2c68ce16f6","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":"2","parents":[],"plain":"$\\mathrm{Er_2Ti_2O_7}$ 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 $\\mathrm{Er_2Ti_2O_7}$ 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":"8e4bec8a3360c242f46e80b11623db9058d1b79a5722dda9c14f8b4592c84d53","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 $\\mathrm{Er_2Ti_2O_7}$?","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"4954614aa8a7f548fa9bfe310670dfbd1ab56c0f87279bb40999594b6f6e594f","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"336e696aacaadd3c789bc5517b107158b40ac96b8d9aab62c971aa3ef2137d35","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"9PnLegxPpNiTr0j4RDUXEbK71DT3ldSM0rfgOAQEcw5lGgiSA2bpGBUyCy7lkJXS6_On6IPFKrmASZpmO3OfAA"},"schema":"pubphys.envelope/1"},"record_hash":"4954614aa8a7f548fa9bfe310670dfbd1ab56c0f87279bb40999594b6f6e594f","leaf_index":2816}