{"paper":{"title":"Universal Quantum Criticality from a Gaussian Variational Manifold","arxiv_id":"2610.26246","primary_cat":"quant-ph","submitted_at":"2026-10-19T12:07:10+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Universal behavior at continuous phase transitions is encoded in long-wavelength fixed-point theories controlled by dimensionality and symmetries.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.64,"id":"s1","own":false,"role":"background","text":"It is a central question for which systems this universal behavior and the underlying long-wavelength description can be captured by a noninteracting theory allowing for analytical and accurate predictions.","hedge":{"p":0.69,"label":"asserted"},"own_p":0.04,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.36,"method":0.0,"result":0.0,"background":0.64,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.67,"id":"s2","own":true,"role":"contribution","text":"In this work we provide a systematic procedure for obtaining the best noninteracting fermionic description of a quantum phase transition through fermionic Gaussian states.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.33,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.67,"interpretation":0.0}},{"i":3,"p":0.83,"id":"s3","own":true,"role":"contribution","text":"We demonstrate the performance of our procedure for the interacting long-range transverse-field Ising chain.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.13,"result":0.04,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.83,"interpretation":0.0}},{"i":4,"p":0.99,"id":"s4","own":true,"role":"result","text":"This formulation reduces the problem to a self-consistent Euler equation that yields a critical line in close agreement with independent numerical benchmarks, while its singular momentum structure provides analytic predictions for continuously varying critical properties.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.31,"quantitative":true,"quantitative_p":0.54,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":5,"p":0.55,"id":"s5","own":true,"role":"result","text":"Yet exact diagonalization shows that Gaussian-state fidelity to the exact ground state is poorest, and non-Gaussianity strongest, near the transition.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.76,"main_claim_p":0.05,"quantitative":true,"quantitative_p":0.85,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.55,"background":0.0,"limitation":0.45,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":6,"p":0.98,"id":"s6","own":true,"role":"interpretation","text":"Thus, accurate predictions for critical properties can emerge from the Gaussian variational description even where its microscopic wave-function approximation is weakest.","hedge":{"p":0.86,"label":"asserted"},"own_p":0.85,"main_claim_p":0.75,"quantitative":false,"quantitative_p":0.22,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.98}}]},"compiled":{"main_claim":{"p":1.0,"text":"Thus, accurate predictions for critical properties can emerge from the Gaussian 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