Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems

Abstract

Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and driving, and hence require a variety of techniques and concepts to describe their topological properties. For instance, depending on the system, topology may be accessed from single-particle Bloch wave functions, Green's functions, or many-body wave functions. We demonstrate that despite this diversity, all topological phase transitions display a universal feature: namely, a divergence of the curvature function that composes the topological invariant at the critical point. This feature can be exploited via a renormalization-group-like methodology to describe topological phase transitions. This approach serves to extend notions of correlation function, critical exponents, scaling laws and universality classes used in Landau theory to characterize topological phase transitions in a unified manner.

arXiv comment7 pages, 3 figures, to appear in Europhysics Letters

References in corpus (63)

• Maximally-localized generalized Wannier functions for composite energy bands
• Unpaired Majorana fermions in quantum wires
• Maximally localized Wannier functions: Theory and applications
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Topological characterization of periodically-driven quantum systems
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
• Identifying Topological Order by Entanglement Entropy
• Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation
• Floquet topological insulators
• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials
• Single particle Green's functions and interacting topological insulators
• Periodic Table for Floquet Topological Insulators
• Mapping topological order in coordinate space
• Bulk-boundary correspondence of topological insulators from their Green's functions
• Floquet generation of Majorana end modes and topological invariants
• The entanglement gap and a new principle of adiabatic continuity
• Extracting Excitations From Model State Entanglement
• First order character and observable signatures of topological quantum phase transitions
• Floquet Majorana and Para-Fermions in Driven Rashba Nanowires
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Fluctuation driven topological Hund insulators
• Theory of photoinduced Floquet Weyl semimetal phases
• Realistic Floquet semimetal with exotic topological linkages between arbitrarily many nodal loops
• Fractional quantum-Hall liquid spontaneously generated by strongly correlated t_2g electrons
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Majorana edge modes in the Kitaev model
• Characterization of topological states via dual multipartite entanglement
• Steady states and edge state transport in topological Floquet-Bloch systems
• Topological Marker Currents in Chern Insulators
• Floquet Weyl semimetals in light-irradiated type-II and hybrid line-node semimetals
• Emergent Weyl nodes and Fermi arcs in a Floquet Weyl semimetal
• Universality classes of topological phase transitions with higher-order band crossing
• Floquet Quantum Criticality
• Entanglement topological invariants for one-dimensional topological superconductors
• Continuous and discontinuous topological quantum phase transitions
• Fractional Chern insulator on a triangular lattice of strongly correlated $t_{2g}$ electrons
• Fractional Chern insulators with strong interactions far exceeding bandgaps
• Edge states reconstruction from strong correlations in quantum spin Hall insulators
• First order topological phase transition of the Haldane--Hubbard model
• Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State
• Universalities of thermodynamic signatures in topological phases
• Scaling Theory of Topological Phase Transitions
• Combined topological and Landau order from strong correlations in Chern bands
• Weakly Interacting Topological Insulators: Quantum Criticality and Renormalization Group Approach
• Universal quantum criticality in static and Floquet-Majorana chains
• Sensing Floquet-Majorana fermions via heat transfer
• Generating quantum multi-criticality in topological insulators by periodic driving
• Edge and bulk localization of Floquet topological superconductors
• Thermodynamic signatures of edge states in topological insulators
• Central Charge of Periodically Driven Critical Kitaev Chains
• Weyl-type topological phase transitions in fractional quantum Hall like systems
• Quantum Phase Transition and Entanglement in Topological Quantum Wires
• Quench Dynamics Across Topological Quantum Phase Transitions
• First-Order Topological Quantum Phase Transition in a Strongly Correlated Ladder
• Staircase to Higher-Order Topological Phase Transitions
• The transport properties of Floquet topological superconductors at the transition from the topological phase to the Anderson localized phase
• $2\pi$-flux loop semimetals
• Quasiparticles as Detector of Topological Quantum Phase Transitions
• Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators

Cited by in corpus (19)

• Unconventional scaling at non-Hermitian critical points
• 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
• Topological phase transitions at finite temperature
• 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
• A supervised learning algorithm for interacting topological insulators based on local curvature
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Topological quantum phase transitions and criticality in a longer-range Kitaev chain
• A renormalization group approach to non-Hermitian topological quantum criticality
• Topological phase transition between non-high symmetry critical phases and curvature function renormalization group
• Curvature function renormalisation, topological phase transitions and multicriticality
• Scaling behavior in a multicritical one-dimensional topological insulator
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
• Thermodynamics of a Higher-Order Topological Insulator
• Interference-induced suppression of particle emission from a Bose-Einstein condensate in lattice with time-periodic modulations