Quantum quench in the attractive regime of the sine-Gordon model

Abstract

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, $\exp \left(\mathrm{i}\beta \Phi /2\right)$, 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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Cited by in corpus (13)

• Preparing and Analyzing Solitons in the sine-Gordon Model with Quantum Gas Microscopes
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Non-monotonic response and light-cone freezing in gapless-to-(partially) gapped quantum quenches of fermionic systems
• Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain
• Josephson oscillations in split one-dimensional Bose gases
• Quantum sine-Gordon dynamics in coupled spin chains
• Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model
• Relaxation dynamics of integrable field theories after a global quantum quench
• Non-equilibrium time evolution in the sine-Gordon model revisited
• Quantum quenches in the sinh-Gordon and Lieb-Liniger models
• Caustics in the sine-Gordon model from quenches in coupled 1D Bose gases