Journal
PHYSICAL REVIEW B
Volume 93, Issue 8, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.93.085416
Keywords
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Funding
- Deutsche Akademie der Naturforscher Leopoldina [LPDS 2013-07, LPDR 2015-01]
- ERC synergy Grant UQUAM
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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.
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