Topological Entanglement-Spectrum Crossing in Quench Dynamics

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• Topological Phases of Matter

Background:

• Understanding quantum quench dynamics is crucial for exploring non-equilibrium quantum systems.
• Topological phases of matter exhibit robust properties protected by symmetries.
• Altland-Zirnbauer classes provide a framework for classifying topological insulators and superconductors.

Purpose of the Study:

• To identify stable (d+1)-dimensional topological structures in d=1 quench dynamics across all Altland-Zirnbauer classes.
• To propose entanglement spectra as a method for detecting dynamical topology.
• To investigate the role of topology in the time evolution of quantum systems.

Main Methods:

• Analysis of quench dynamics in one-dimensional systems belonging to Altland-Zirnbauer classes.
• Focus on systems in symmetry classes BDI and D.
• Examination of entanglement spectra, including single-particle and many-body spectra.
• Assessment of stability against symmetry-preserving disorder.

Main Results:

• Stable topological structures underlying quench dynamics were identified for all Altland-Zirnbauer classes in d=1.
• Entanglement spectrum crossings were observed during quantum quenches between different symmetry-protected topological phases in classes BDI and D.
• These crossings are stable against disorder and reflect Z (BDI) and Z2 (D) topological characterizations.
• The topological origin of degeneracies in the many-body entanglement spectrum of the transverse-field Ising model was revealed.

Conclusions:

• Dynamical topology in quench processes can be detected using entanglement spectra.
• Entanglement spectrum crossings serve as robust indicators of topological phases.
• This work provides a foundation for understanding topology's role in non-equilibrium quantum dynamics.
• Experimental verification in ultracold atoms and trapped ions is feasible.