Return amplitude after a quantum quench in the XY chain. (20th August 2019)

• Record Type: Journal Article
• Authors: Najafi, Khadijeh; Rajabpour, M A; Viti, Jacopo
• Is Part Of: Journal of statistical mechanics. (2019:Aug.)
• Publication Date: 2019-08-20
• Subjects: 2; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ab3413
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We determine an exact formula for the transition amplitude between any two arbitrary eigenstates of the local z -magnetization operators in the quantum XY chain. We further use this formula to obtain an analytical expression for the return amplitude of fully polarized states and the Néel state on a ring of length L . Then, we investigate finite-size effects in the return amplitude: in particular quasi-particle interference halfway along the ring, a phenomenon that has been dubbed traversal (Essler and Fagotti 2016 J. Stat. Mech . 064002). We show that the traversal time and the features of the return amplitude at the traversal time depend on the initial state and on the parity of L . Finally, we briefly discuss non-analyticities in time of the decay rates in the thermodynamic limit, which are known as dynamical phase transitions.