Confinement of sine-Gordon solitons in a perturbed sine-Gordon model

The quantum sine-Gordon model is one of the paradigmatic models of an integrable quantum field theory (QFT). When perturbed by a higher harmonic, the model is no longer integrable. However, it exhibits a rich set of non-perturbative phenomena ranging from confinement of sine-Gordon solitons to an Ising-type phase transition. In this work, we numerically analyze the confinement of sine-Gordon solitons using the XYZ spin-chain regularization for the model. To that end, we consider a global quantum quench and compute the time dependence of the correlation functions and the entanglement entropy using the time evolution block decimation technique. The presence of the perturbation leads to the formation of mesonic bound states akin to what happens in t'Hooft's 1+1D model of quantum chromodynamics and constitutes a rich generalization of the analogous phenomena in the quantum Ising model. We compute the mass spectra of the mesons numerically. We perform semi-classical analytic computations at the free-fermion point and verify our numerical computations with the analytical predictions.