Scaling Theory of Topological Phase Transitions

Abstract

Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc.) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.

6 pages, 3 figures

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Cited by in corpus (35)

• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Universality classes of topological phase transitions with higher-order band crossing
• Measurement of Topological Order based on Metric-Curvature Correspondence
• Universal topological marker
• Weakly Interacting Topological Insulators: Quantum Criticality and Renormalization Group Approach
• Universal quantum criticality in static and Floquet-Majorana chains
• Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
• Generating quantum multi-criticality in topological insulators by periodic driving
• Fidelity susceptibility near topological phase transitions in quantum walks
• Kibble-Zurek behavior in disordered Chern insulators
• Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems
• Weyl-type topological phase transitions in fractional quantum Hall like systems
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Multi-critical topological transition at quantum criticality
• Anomalous fractal scaling in two-dimensional electric networks
• Unification of topological invariants in Dirac models
• Signatures of topological phase transition on a quantum critical line
• Quench dynamics and scaling laws in topological nodal loop semimetals
• Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
• Edge mode manipulation through commensurate multifrequency driving
• Phase transitions and scale invariance in topological Anderson insulators
• A supervised learning algorithm for interacting topological insulators based on local curvature
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• A renormalization group approach to non-Hermitian topological quantum criticality
• Topological phase transition between non-high symmetry critical phases and curvature function renormalization group
• Multicriticality in a one-dimensional topological band insulator
• Slow quenches in Chern insulator ribbons
• Curvature function renormalisation, topological phase transitions and multicriticality
• Renormalization group approach to symmetry protected topological phases
• Scaling behavior in a multicritical one-dimensional topological insulator
• Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators
• Reentrant topological phases and spin density wave induced by 1D moiré potentials
• Reentrant topological phases and entanglement scalings in moiré-modulated extended Su-Schrieffer-Heeger Model
• Non-necessity of band inversion process in 2D topological insulators for bulk gapless states and topological phase transitions
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions