Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

Year: 2014

Authors: Canovi E., Ercolessi E., Naldesi P., Taddia L., Vodola D.

Autors Affiliation: Institut fur Theoretische Physik III, Universitat Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany;
Dipartimento di Fisica e Astronomia dell’Università di Bologna and INFN, Sezione di Bologna, Via Irnerio 46, 40127 Bologna, Italy;
IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, Strasbourg, France

Abstract: We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the transverse-field Ising model with a time-dependent magnetic field, which is linearly tuned on a time scale iota. The time evolution of the entanglement entropy displays different regimes depending on the value of iota, showing also oscillations which depend on the instantaneous energy spectrum. The entanglement spectrum is characterized by a rich dynamics where multiple crossings take place with a gap-dependent frequency. Moreover, we investigate the Kibble-Zurek scaling of the entanglement entropy and Schmidt gap.


Volume: 89 (10)      Pages from: 104303  to: 104303

More Information: We thank D. Bianchini, T. Caneva, C. Degli Esposti Boschi, M. Dalmonte, L. Ferrari, A. Lazarides, F. Ortolani, G. Zonzo and the participants in the mini-workshop \”Collective quantum phenomena: Methods and tools from entanglement theory,\” organized by F. Illuminati in Salerno, for enlightening discussions. E.C. acknowledges financial support from DPG through Project No. SFB/TRR21 and Dipartimento di Fisica e Astronomia dell\’Università di Fisica e Astronomia dell\’Universita di Bologna for hospitality.
KeyWords: quantum; many-body; dynamics; entanglement; cosmological experiments
DOI: 10.1103/PhysRevB.89.104303

Citations: 47
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