Bethe ansatz study of two-dimensional soliton lattice melting

We study the melting of incommensurate soliton lattice using the exact Bethe ansatz solution of one-dimensional quantum sine-Gordon Hamiltonian with U(1) coupling. The elastic moduli of soliton lattice are obtained and their asymptotic behaviors are explicitly calculated both at zero and finite temperature. We have obtained the thermodynamic phase boundaries of the soliton lattice and shown that the direct commensurate–incommensurate transitions are intervened by the fluid phase for T>0 as predicted by Coppersmith et al. [Coppersmith et al., Phys. Rev. Lett. 46 (1981) 549. [1]] for n≤2.