The phase diagram of the one-dimensional quantum sine-Gordon system ($β^{2}=4π)$ with a linear spatial modulation

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/17576The one-dimensional quantum sine-Gordon system with a linear spatial modulation is investigated in a special case, $β^{2}$ =4$π$. The model is tranformed into a massive Thirring model and then is exactly diagonalized, the energy spetrum of the model is obtained. Our result clearly demonstrates that cancelling the cosine term without any considering is unadvisable.4 pages in texStrongly Correlated ElectronsThe phase diagram of the one-dimensional quantum sine-Gordon system ($β^{2}=4π)$ with a linear spatial modulationtext