The critical properties of a modulated quantum sine-Gordon model

A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Cordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters (alphaLambda(-2), beta(2)) plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at beta(2) = 4pi, the IC phase can only appear for beta(2) greater than or equal to 4pi and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter alphaLambda(-2). The transition is of the continuous type on the mrtical part of the boundary, while it is of the first order on the boundary beta(2) > 4pi.