Dynamical topological order parameters far from equilibrium
By J. C. Budich, Markus Heyl. 2015
186 citations recorded by the source corpus.
We introduce a topological quantum number -- coined dynamical topological order parameter (DTOP) -- that is dynamically defined in the real-time evolution of a quantum many-body system and represented by a momentum space winding number of the Pancharatnam geometric phase. Our construction goes conceptually beyond the standard notion of topological invariants characterizing the wave-function of a system, which are constants of motion under coherent time evolution. In particular, we show that the DTOP can change its integer value at discrete times where so called dynamical quantum phase transitions occur, thus serving as a dynamical analog of an order parameter. Interestingly, studying quantum quenches in one-dimensional two-banded Bogoliubov de Gennes models, we find that the DTOP is capable of resolving if the topology of the system Hamiltonian has changed over the quench. Furthermore, we investigate the relation of the DTOP to the dynamics of the string order parameter that characterizes the topology of such systems in thermal equilibrium.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/a40681b6d0a3fff14831176f1b0b3b2b9cf48b4f
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Floquet topological transitions in a driven one-dimensional topological insulator (2015, background): “More generally, there is a surge of interest in the physics of topological properties far from equilibrium [30,38].”