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arXiv:1602.08269 · Journal of Statistical Mechanics Theory and Experiment

Quantum quenches in the sinh-Gordon model: steady state and one-point correlation functions

Bruno Bertini, Lorenzo Piroli, Pasquale Calabrese

Published Jun 1, 2016• 98 citations
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Abstract

Abstract. We consider quantum quenches to the sinh-Gordon integrable quantum field theory from a particular class of initial states. Our analysis includes the case of mass and interaction quenches starting from a non-interacting theory. By means of the recently developed quench action method, we fully characterize the stationary state reached at long times after the quench in terms of the corresponding rapidity distribution. We also provide exact results for the expectation values of arbitrary vertex operators in the post-quench stationary state by proposing a formula based on the analogy with the standard thermodynamic Bethe ansatz. Finally, we comment on the behavior of the post-quench stationary state under the mapping between the sinh-Gordon field theory and the one-dimensional Lieb–Liniger model.

DOI
10.1088/1742-5468/2016/06/063102

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We consider the time evolution in the repulsive sine-Gordon quantum field theory after the system is prepared in a particular class of initial states. We focus on the time dependence of the one-point function of the semi-local operator exp⁡(i β Φ(x)/2)\exp\big(i\ β\ Φ(x)/2\big)exp(i β Φ(x)/2). By using two different methods based on form-factor expansions, we show that this expectation value decays to zero exponentially, and we determine the decay rate by analytical means. Our methods generalise to other correlation functions and integrable models.