{"arxiv_id":"cond-mat/0404327","incoming":{"papers":37,"sentences":79,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1712.04943","title":"Localization of Extended Quantum Objects","url":"/paper/1712.04943","section":"Lattice Gauge Theory for a Superconductor","sentence":"Our analysis is an adaptation of [ref] to three spatial dimensions, formulated entirely on a lattice.","intent_p":0.98,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":4,"sentences":6,"quotes":[{"arxiv_id":"1301.7072","title":"QCD as a topologically ordered system","url":"/paper/1301.7072","section":"BF theory for the deformed QCD. 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we are not aware that the following connection between $BF$ theory and surface Dirac fermions or topological insulators has been made before.","intent_p":0.95,"contests_p":null},{"arxiv_id":"1301.7072","title":"QCD as a topologically ordered system","url":"/paper/1301.7072","section":"Differences and Similarities between CM systems and deformed QCD","sentence":"At the same time, if the Euclidean space $ℝ^3$ in eq.([ref]) is additionally compactified on a large torus, i.e. $ℝ^3→𝕋^2×ℝ^1$, than one should expect an additional topological $ℤ_2$ symmetry for $SU(2)$, in close analogy with the behaviour of a CM system [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"2107.08753","title":"Topological axion electrodynamics and 4-group symmetry","url":"/paper/2107.08753","section":"Topological order in bulk","sentence":"We remark that this fractional AB phase is different from a $Z_q$ AB phase of an Abelian Higgs model without an axion [ref] , due to the presence of the axion-photon coupling deforming the 1-form symmetry.","intent_p":0.96,"contests_p":null},{"arxiv_id":"1308.1960","title":"Maxwell Theory on a Compact Manifold as a Topologically Ordered System","url":"/paper/1308.1960","section":"“BF\" formulation of the Maxwell system","sentence":"Therefore, these massless photons can be completely ignored in our studies of the topological properties of the partition function, similar to decoupling of the massless phonons (which are in fact responsible for the mere existence of a gap) in treatment of the topologically ordered superconductors [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"1408.5911","title":"Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation","url":"/paper/1408.5911","section":"Conclusion","sentence":"A similar low-energy description for superconductors was developed in [ref] , with the important difference that for the superfluid the action is not purely topological due to the presence of a gapless Goldstone mode.","intent_p":0.99,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1610.03911","title":"Zoo of quantum-topological phases of matter","url":"/paper/1610.03911","section":"Superconducting states (with dynamical electromagnetism)","sentence":"Superconducting order (in real life) is an topological order (or more precisely a $Z_2$ topological order or $Z_2$ gauge theory) [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"1210.1281","title":"Topological order: from long-range entangled quantum matter to an unification of light and electrons","url":"/paper/1210.1281","section":"The discovery of topological order","sentence":"The real-life superconductors, having a $Z_2$ topological order, [ref] were first experimentally discovered topologically ordered states.[Note that real-life superconductivity can be described by the Ginzburg-Landau theory with a dynamical $U(1)$ gauge field, which become a $Z_2$ gauge theory at low energies; and a $Z_2$ gauge theory is an effective theory of $Z_2$ topological order. ]","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":11,"sentences":17,"quotes":[{"arxiv_id":"1407.3804","title":"Topological order and Berry connection for the Maxwell Vacuum on a four-torus","url":"/paper/1407.3804","section":"Introduction. Motivation.","sentence":"Furthermore, it demonstrates many features of topologically ordered systems, which were initially introduced in context of condensed matter (CM) systems, see original papers [ref] and recent reviews [ref] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"1903.06389","title":"Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system","url":"/paper/1903.06389","section":"Topological order in $U(1)$ gauge theory","sentence":"We here review the appearance of topological order in the low-energy effective theory of the Abelian Higgs model in $(3+1)$ dimensions [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"1011.3485","title":"Topological BF field theory description of topological insulators","url":"/paper/1011.3485","section":"3D $BF$ theory","sentence":"The most general form of 3D $BF$ theory includes a one-form gauge field $a_μ$, an antisymmetric two-form gauge field $b_μν$, and corresponding sources $j^μ$, $Σ^μν$ [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"1708.04626","title":"Fermionic spinon theory of square lattice spin liquids near the N\\'eel state","url":"/paper/1708.04626","section":"Introduction","sentence":"Soon after, `$ℤ_2$ spin liquids' were proposed [ref] : their topological order is compatible with time-reversal symmetry, and exactly solvable examples were later found in Kitaev's toric code and honeycomb lattice models [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"1308.1960","title":"Maxwell Theory on a Compact Manifold as a Topologically Ordered System","url":"/paper/1308.1960","section":"Introduction. 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