Universal topological quench dynamics for Z₂ topological phases.

Area of Science:

• Condensed Matter Physics
• Quantum Dynamics
• Topological Phases

Background:

• Free-fermion topological phases, characterized by Z2 invariants, encompass states like time-reversal invariant topological insulators, typically defined by equilibrium ground states.
• A fundamental question exists regarding the correspondence between these equilibrium topological phases and far-from-equilibrium quantum dynamics.

Purpose of the Study:

• To uncover universal topological quench dynamics that universally link to equilibrium topological phases.
• To establish a general framework for characterizing these dynamics across different dimensions and symmetry classes within the tenfold way.

Main Methods:

• Development of a general theoretical framework to connect equilibrium topological phases with dynamical phenomena.
• Characterization of d-dimensional topological phases using Dirac-type Hamiltonians and Z2 invariants defined at high-symmetry momenta.
• Identification of topology reduced to highest-order band-inversion surfaces at discrete Brillouin zone momenta.

Main Results:

• A novel result shows that dimension-reduced topology at specific momenta uniquely corresponds to topological patterns in far-from-equilibrium quantum dynamics.
• This dimension-reduced topology serves as a dynamical hallmark for equilibrium topological phases.
• The framework successfully characterizes the full tenfold classes of topological phases.

Conclusions:

• The study establishes a universal correspondence between equilibrium topological phases and topological quench dynamics.
• This work provides a dynamical characterization for all tenfold topological phase classes.
• The findings can be extended to broader topological phases, including those protected by lattice symmetries and in non-Dirac systems, advancing both theoretical and experimental research.