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Subject Item
dbr:Curvature_Renormalization_Group_Method
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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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62878887
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1076712929
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dbr:Reciprocal_lattice dbr:Geometric_phase dbr:Differential_equation dbr:Berry_connection_and_curvature dbr:Renormalization_group dbr:Landau_theory dbr:Quantum_mechanics dbr:Critical_exponent dbr:Surface_states dbr:Topological_insulator dbr:Topological_invariant dbc:Theoretical_physics dbr:Topological_order dbr:Ground_state dbr:Floquet_theory dbr:Magnetic_susceptibility dbr:Symmetry_point_group dbr:Majorana_fermion n9:BerryConnectionABCD1234.ogv dbr:Periodic_table_of_topological_invariants n9:Square-wave-Kitaev.pdf dbr:Position_and_momentum_space dbr:Universality_classes dbr:Lorentzian_distribution dbr:Phase_boundaries dbr:Fourier_transform dbr:Order_parameter dbr:Theoretical_physics dbr:Universality_(dynamical_systems) dbr:Quantum_phase_transition dbr:Scaling_law dbr:Vector_flow dbr:Ferrimagnetism dbr:Wannier_function dbr:Wave_function dbr:Critical_phenomena dbr:Topological_quantum_number dbr:Hamiltonian_(quantum_mechanics) dbr:Zero_temperature dbr:Degeneracy_(quantum_mechanics) dbr:Dirac_matter dbr:Correlation_function_(statistical_mechanics)
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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 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.
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wikipedia-en:Curvature_Renormalization_Group_Method
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dbr:Alexei_Kitaev
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dbr:Curvature_Renormalization_Group_Method
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