{"paper":{"title":"Scale invariance of the polaron energy at the Mott-superfluid critical point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The energy of a weakly interacting impurity in a lattice Bose gas stays constant under size rescaling at the Mott-superfluid transition point.","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.quant-gas","authors_text":"Alessio Recati, C. J. Bradly, Georg M. Bruun, Joachim Brand, Matija \\v{C}ufar, Ragheed Alhyder, Victor E. Colussi","submitted_at":"2026-04-20T05:23:55Z","abstract_excerpt":"Continuous quantum phase transitions are characterized by an order parameter and correlation functions that are often challenging to access experimentally or in direct numerical simulations. The energy of an added impurity can on the other hand be probed by established polaron spectroscopy, or numerically with Monte Carlo methods. We provide evidence from ground-state quantum Monte Carlo calculations that the energy of a mobile impurity interacting weakly with a surrounding lattice Bose gas provides access to the critical behavior of the Mott insulator-superfluid phase transition. Finite-size "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Finite-size scaling of the energy reveals that its value is scale invariant at the critical point of the quantum phase transition, and we extract a scaling exponent that is currently unexplained by theory.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The impurity interacts weakly enough that it does not appreciably shift the location or nature of the underlying Mott-superfluid transition, and finite-size scaling from accessible lattice sizes reliably extrapolates to the thermodynamic limit at criticality.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Ground-state quantum Monte Carlo calculations demonstrate scale invariance of the polaron energy at the Mott-superfluid critical point in a lattice Bose gas and extract an unexplained scaling exponent.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The energy of a weakly interacting impurity in a lattice Bose gas stays constant under size rescaling at the Mott-superfluid transition point.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8e88ced5b30c49103d4576f7cc306e52e1569ef2be52db1f433be2417896c8a7"},"source":{"id":"2604.17824","kind":"arxiv","version":2},"verdict":{"id":"80acbc80-39fa-44e3-8d46-fb4fb6fbcaec","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:13:52.660887Z","strongest_claim":"Finite-size scaling of the energy reveals that its value is scale invariant at the critical point of the quantum phase transition, and we extract a scaling exponent that is currently unexplained by theory.","one_line_summary":"Ground-state quantum Monte Carlo calculations demonstrate scale invariance of the polaron energy at the Mott-superfluid critical point in a lattice Bose gas and extract an unexplained scaling exponent.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The impurity interacts weakly enough that it does not appreciably shift the location or nature of the underlying Mott-superfluid transition, and finite-size scaling from accessible lattice sizes reliably extrapolates to the thermodynamic limit at criticality.","pith_extraction_headline":"The energy of a weakly interacting impurity in a lattice Bose gas stays constant under size rescaling at the Mott-superfluid transition point."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.17824/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":50,"sample":[{"doi":"","year":2011,"title":"Sachdev,Quantum Phase Transitions, 2nd ed","work_id":"f7dbdf27-02f7-46ba-a13b-3fd82488cbbe","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1972,"title":"M. E. Fisher and M. N. Barber, Scaling Theory for Finite- Size Effects in the Critical Region, Physical Review Let- ters28, 1516 (1972)","work_id":"90eff46b-ac14-412e-b3c1-e46575360d8e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"Cardy, ed.,Finite-Size Scaling, Current Physics – Sources and Comments, Vol","work_id":"3dd46c40-5933-4260-befe-5e51e0d7c331","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2069,"title":"Vojta, Quantum phase transitions, Reports on Progress in Physics66, 2069 (2003)","work_id":"5f5dbedf-dd5d-49a3-bf0f-85b6e846f592","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"A. Camacho-Guardian, N. Goldman, P. Massignan, and G. M. Bruun, Dropping an impurity into a chern insula- tor: A polaron view on topological matter, Phys. Rev. B 99, 081105 (2019)","work_id":"4cee2c53-997d-4c33-af9a-341680bf72e3","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":50,"snapshot_sha256":"6f9982801d6b638dbe5d1ed333fca22a6f30fc9f74d330cad9233758981103e4","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6f36c167a48dd905d93d949cd60297181613f013087bcfc35178e78bcdad9c4a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}