About: Curvature Renormalization Group Method

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In theoretical physics, the curvature renormalization group (CRG) method is an analytical approach to determine the phase boundaries and the critical behavior of topological systems. Topological phases are phases of matter that appear in certain quantum mechanical systems at zero temperature because of a robust degeneracy in the ground-state wave function. They are called topological because they can be described by different (discrete) values of a nonlocal topological invariant. This is to contrast with non-topological phases of matter (e.g. ferromagnetism) that can be described by different values of a local order parameter. States with different values of the topological invariant cannot change into each other without a phase transition. The topological invariant is constructed from a c

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rdfs:label	Curvature Renormalization Group Method (en)
rdfs:comment	In theoretical physics, the curvature renormalization group (CRG) method is an analytical approach to determine the phase boundaries and the critical behavior of topological systems. Topological phases are phases of matter that appear in certain quantum mechanical systems at zero temperature because of a robust degeneracy in the ground-state wave function. They are called topological because they can be described by different (discrete) values of a nonlocal topological invariant. This is to contrast with non-topological phases of matter (e.g. ferromagnetism) that can be described by different values of a local order parameter. States with different values of the topological invariant cannot change into each other without a phase transition. The topological invariant is constructed from a c (en)
dcterms:subject	Theoretical physics
Wikipage page ID	62878887 (xsd:integer)
Wikipage revision ID	1076712929 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum mechanics Renormalization group Reciprocal lattice Topological insulator Topological invariant Critical exponent Theoretical physics Geometric phase Topological order Surface states Correlation function (statistical mechanics) Critical phenomena Phase boundaries Berry connection and curvature Magnetic susceptibility Hamiltonian (quantum mechanics) Periodic table of topological invariants Theoretical physics Wave function Landau theory Fourier transform Differential equation Dirac matter Floquet theory Ground state Quantum phase transition Real space Ferrimagnetism Majorana fermion Scaling law Universality (dynamical systems) Wannier function Topological quantum number Vector flow Order parameter Universality classes Symmetry point group Degeneracy (quantum mechanics) Lorentzian distribution Zero temperature dbr:File:BerryConnectionABCD1234.ogv dbr:File:Square-wave-Kitaev.pdf
sameAs	Curvature Renormalization Group Method Curvature Renormalization Group Method
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	In theoretical physics, the curvature renormalization group (CRG) method is an analytical approach to determine the phase boundaries and the critical behavior of topological systems. Topological phases are phases of matter that appear in certain quantum mechanical systems at zero temperature because of a robust degeneracy in the ground-state wave function. They are called topological because they can be described by different (discrete) values of a nonlocal topological invariant. This is to contrast with non-topological phases of matter (e.g. ferromagnetism) that can be described by different values of a local order parameter. States with different values of the topological invariant cannot change into each other without a phase transition. The topological invariant is constructed from a curvature function that can be calculated from the bulk Hamiltonian of the system. At the phase transition, the curvature function diverges, and the topological invariant correspondingly jumps abruptly from one value to another. The CRG method works by detecting the divergence in the curvature function, and thus determining the boundaries between different topological phases. Furthermore, from the divergence of the curvature function, it extracts scaling laws that describe the critical behavior, i.e. how different quantities (such as susceptibility or correlation length) behave as the topological phase transition is approached. The CRG method has been successfully applied to a variety of static, periodically driven, weakly and strongly interacting systems to classify the nature of the corresponding topological phase transitions. (en)
prov:wasDerivedFrom	wikipedia-en:Curvature_Renormalization_Group_Method?oldid=1076712929&ns=0
page length (characters) of wiki page	15820 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Curvature_Renormalization_Group_Method
is Link from a Wikipage to another Wikipage of	Alexei Kitaev
is foaf:primaryTopic of	wikipedia-en:Curvature_Renormalization_Group_Method

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