{"id":"W2247716444","doi":"","title":"Translation-symmetry-protected topological orders in quantum spin systems","year":2009,"lang":"en","type":"article","venue":"DSpace@MIT (Massachusetts Institute of Technology)","topic":"Topological Materials and Phenomena","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Perimeter Institute","funders":"","keywords":"Symmetry protected topological order; Physics; Topological order; Topological entropy in physics; Topology (electrical circuits); Lattice (music); Translational symmetry; Topological degeneracy; Homogeneous space; Topological quantum number; Quantum mechanics; Quantum; Condensed matter physics; Mathematics; Geometry; Combinatorics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000225176,0.000188746,0.0002805112,0.0005893759,0.0007483377,0.0009519718,0.000414483,0.0005637503,0.001388443],"category_scores_gemma":[0.000609761,0.0001469584,0.0003874286,0.0002443693,0.001366127,0.001326479,0.0003819014,0.0003265086,0.0001041329],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003604239,"about_ca_system_score_gemma":0.0004668873,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004434294,"about_ca_topic_score_gemma":0.0004894872,"domain_scores_codex":[0.9998392,0.00003346499,0.000009160241,0.00001466768,0.00005743964,0.00004598959],"domain_scores_gemma":[0.9997591,0.00005880901,0.0000528797,0.00007126723,0.00002579315,0.00003209495],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000175502,0.0001449445,0.004134273,0.0001136888,0.00003264564,0.0006576771,0.0003610841,0.03563221,0.03476662,0.9150087,0.0006000258,0.008372614],"study_design_scores_gemma":[0.0001692869,0.0003413278,0.005160193,0.00003166455,0.00003573329,0.0006060242,0.0004706531,0.3680503,0.01876794,0.6031981,0.003106303,0.00006251979],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9833348,0.0001308815,0.01053476,0.00009425016,0.00002224892,0.0000164459,0.00002188945,0.00005111104,0.005793602],"genre_scores_gemma":[0.9974082,0.00004681985,0.002142958,0.00001216992,0.00001146455,0.00001089243,0.00002373792,0.000007910425,0.0003359476],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001388443,"threshold_uncertainty_score":0.004644752,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01808127742477269,"score_gpt":0.2599922867959057,"score_spread":0.2419110093711331,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}