The Critical Properties of a Modulated Quantum Sine-Gordon Model

A new procedure of trial variational wave functional is proposed for investigating the mass renormailzation and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters (αΛ−2, β2) plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at β2 = 4π, the IC phase can only appear for β2 ≥ 4π and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter αΛ−2. The transition is of the continuous type on the vertical part of the boundary, while it is of the first order on the boundary for β2 > 4π. PACS: 05.70.Jk, 68.10.-m,87.22.Bt