{"arxiv_id":"1403.2018","incoming":{"papers":27,"sentences":32,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1606.08482","title":"Exactly Solvable Models for Symmetry-Enriched Topological Phases","url":"/paper/1606.08482","section":"Introduction","sentence":"We further extend these ideas to construct fixed-point wave functions for anomalous surface topological orders of 3D SPT phases described by group cohomology models [ref] .","intent_p":0.87,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":9,"sentences":10,"quotes":[{"arxiv_id":"2109.10051","title":"Sigma-model analysis of $SU(3)$ antiferromagnetic spins on the triangular lattice","url":"/paper/2109.10051","section":"Phase transition and constraints by anomaly matching","sentence":"Thanks to theoretical developments of symmetry-protected topological (SPT) phases, we now obtain much deep understandings of anomaly matching condition [ref] (see, for example, Refs. [ref] for some of recent applications).","intent_p":0.9,"contests_p":null},{"arxiv_id":"2404.16803","title":"Non-supersymmetric duality cascade of QCD(BF) via semiclassics on $\\mathbb{R}^2\\times T^2$ with the baryon-'t Hooft flux","url":"/paper/2404.16803","section":"Introduction and Summary","sentence":"Indeed, the phase diagram of the QCD(BF) has been investigated from the anomaly matching as well as from some calculable limits [ref] (See also Refs. [ref] for recent developments of anomaly matching and global inconsistency), and these studies uncover its nontrivial phase diagram.","intent_p":0.82,"contests_p":null},{"arxiv_id":"1903.04014","title":"High-temperature domain walls of QCD with imaginary chemical potentials","url":"/paper/1903.04014","section":"Introduction","sentence":"Thanks to the development of symmetry-protected topological phases [ref] , people understand that the applicability of 't Hooft anomaly matching condition is much broader, and anomaly matching conditions are providing new insights on strongly-coupled QFTs [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"2307.13954","title":"Semiclassical analysis of the bifundamental QCD on $\\mathbb{R}^2\\times T^2$ with 't Hooft flux","url":"/paper/2307.13954","section":"Introduction","sentence":"The phase diagram has been investigated from the recent developments of the anomaly matching [ref] or global inconsistency [ref] and also from various calculable limits.","intent_p":0.95,"contests_p":null},{"arxiv_id":"2001.07373","title":"Global anomaly matching in higher-dimensional $\\mathbb{CP}^{N-1}$ model","url":"/paper/2001.07373","section":"Introduction","sentence":"Recently, new 't Hooft anomalies involving generalized global symmetries such as discrete symmetries [ref] and higher-form symmetries [ref] are found and applied to a large variety of systems both in condensed matter physics [ref] and high-energy physics [ref] .","intent_p":0.94,"contests_p":null}]}],"unlabelled_sentences":21},"outgoing":{"papers":10,"sentences":29,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":1,"sentences":4,"quotes":[{"arxiv_id":"1302.2634","title":"Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids","url":"/paper/1302.2634","section":"$ℤ^A_2 ×ℤ^B_2 ×ℤ^C_2$ symmetric case","sentence":"As before, we begin with identifying a new anyon excitation $l_v$ in the charge lattice [ref] . l⃗_v = K δϕ⃗/2π = (0,0,0,1/2)^T,","intent_p":0.89,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":7,"sentences":7,"quotes":[{"arxiv_id":"1309.0515","title":"Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models","url":"/paper/1309.0515","section":"Theory of Surface state","sentence":"It has been shown that the three-dimensional bosonic SPT phases can be successfully studied by the semi-classical O(5) non-linear sigma model supplemented by the topological $Θ$-term [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"1302.2634","title":"Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids","url":"/paper/1302.2634","section":"Comparison to (2+1)-dimensional topological phases","sentence":"As before we assume $G_1$ is “conventional” [ref] and shifts the phases of the quasi-particle excitations.","intent_p":0.83,"contests_p":null},{"arxiv_id":"1210.0909","title":"Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QED_3$ and anyon superfluid","url":"/paper/1210.0909","section":"Introduction","sentence":"The other quantum disordered states, which has been studied extensively recently, are so-called a Symmetry Protected Topological (SPT) phase [ref] .","intent_p":0.9,"contests_p":null},{"arxiv_id":"1306.3223","title":"Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator","url":"/paper/1306.3223","section":"Introduction","sentence":"The other quantum disordered states, which has been studied extensively recently, are so-called a Symmetry Protected Topological (SPT) phase [ref] .","intent_p":0.9,"contests_p":null},{"arxiv_id":"1106.4772","title":"Symmetry protected topological orders and the group cohomology of their symmetry group","url":"/paper/1106.4772","section":"Introduction","sentence":"The other quantum disordered states, which has been studied extensively recently, are so-called a Symmetry Protected Topological (SPT) phase [ref] .","intent_p":0.9,"contests_p":null}]}],"unlabelled_sentences":18},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1403.2018"}}