We explain how to apply a Gaussian-preserving operator to a fermionic Gaussian state. We use this method to study the evolution of the entanglement entropy of an Ising spin chain undergoing a quantum-jump dynamics with string measurement operators. We find that, for finite-range string operators, the asymptotic entanglement entropy exhibits a crossover from a logarithmic to an area-law scaling with the system size, depending on the Hamiltonian parameters as well as on the measurement strength. For ranges of the string which scale extensively with the system size, the asymptotic entanglement entropy shows a volume-law scaling, independently of the measurement strength and the Hamiltonian dynamics. The same behavior is observed for the measurement-only dynamics, suggesting that measurements may play a leading role in this context.
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- 1 Università degli Studi di Catania / University of Catania
- 2 Università di Pisa / University of Pisa [UniPi]
- 3 INFN Sezione di Pisa
- 4 Università degli Studi di Napoli Federico II / University of Naples Federico II
- 5 Scuola Superiore Meridionale [SSM]
- Ministero dell'Università e della Ricerca
- Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) (through Organization: Ministero dell'Istruzione, dell'Università e della Ricerca / Ministry of Education, Universities and Research [MIUR])