Universal quantum criticality in static and Floquet-Majorana chains

Abstract

The topological phase transitions in static and periodically driven Kitaev chains are investigated by means of a renormalization group (RG) approach. These transitions, across which the numbers of static or Floquet Majorana edge modes change, are accompanied by divergences of the relevant Berry connections. These divergences at certain high symmetry points in momentum space form the basis of the RG approach, through which topological phase boundaries are identified as a function of system parameters. We also introduce several aspects to characterize the quantum criticality of the topological phase transitions in both static and Floquet systems: a correlation function that measures the overlap of Majorana-Wannier functions, the decay length of the Majorana edge mode and a scaling law relating the critical exponents. These indicate a common universal critical behavior for topological phase transitions, in both static and periodically driven chains. For the latter, the RG flows additionally display intriguing features related to gap closures at non-high symmetry points due to momentarily frozen dynamics.

14 pages, 12 figures

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Cited by in corpus (31)

• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Universality classes of topological phase transitions with higher-order band crossing
• Floquet dynamical quantum phase transitions under synchronized periodic driving
• Generating quantum multi-criticality in topological insulators by periodic driving
• Fidelity susceptibility near topological phase transitions in quantum walks
• Edge and bulk localization of Floquet topological superconductors
• Topological characterization and stability of Floquet Majorana modes in Rashba nanowire
• Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems
• Multi-critical topological transition at quantum criticality
• Unification of topological invariants in Dirac models
• Topological phase transitions at finite temperature
• Signatures of topological phase transition on a quantum critical line
• Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
• Phase transitions and scale invariance in topological Anderson insulators
• Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence
• Edge mode manipulation through commensurate multifrequency driving
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Topological quantum phase transitions and criticality in a longer-range Kitaev chain
• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
• Topological phase transition between non-high symmetry critical phases and curvature function renormalization group
• Quasiperiodic disorder induced critical phases in a periodically driven dimerized $p$-wave Kitaev chain
• Curvature function renormalisation, topological phase transitions and multicriticality
• Scaling behavior in a multicritical one-dimensional topological insulator
• Topological properties of a periodically driven Creutz ladder
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
• Interaction Driven Floquet Engineering of Topological Superconductivity in Rashba Nanowires
• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Emerging topological characterization in non-equilibrium states of quenched Kitaev chains
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Structure and scaling of Kitaev chain across a quantum critical point in real space