Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/aa8c2e
Keywords
quantum quenches; form factors; integrable spin chains and vertex models
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Funding
- Dutch Ministry of Education, Culture and Science (OCW)
- Foundation for Fundamental Research on Matter (FOM), Netherlands Organisation for Scientific Research (NWO) [14PR3168]
- European Unions Horizon under the Marie Sklodowska-Curie grant agreement [750092]
- Marie Curie Actions (MSCA) [750092] Funding Source: Marie Curie Actions (MSCA)
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We study the dynamics of the sine-Gordon model after a quantum quench into the attractive regime, where the spectrum consists of solitons, antisolitons and breathers. In particular, we analyse the time-dependent expectation value of the vertex operator, exp (i beta Phi/2), starting from an initial state in the 'squeezed state form' corresponding to integrable boundary conditions. Using an expansion in terms of exact form factors, we compute analytically the leading contributions to this expectation value at late times. We show that form factors containing breathers only contribute to the late-time dynamics if the initial state exhibits zero-momentum breather states. The leading terms at late times exponentially decay, and we compute the different decay rates. In addition, the late-time contributions from the zero-momentum breathers display oscillatory behaviour, with the oscillation frequency given by the breather mass renormalised by interaction effects. Using our result, we compute the low-energy contributions to the power spectrum of the vertex operator. The oscillatory terms in the expectation value are shown to produce smooth peaks in the power spectrum located near the values of the bare breather masses.
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