Lock-in transitions and charge transfer in one-dimensional fermion systems

The one-dimensional quantum sine-Gordon Hamiltonian with a density rho _s of solitons is studied. rho _s( mu ) is the order parameter for the lock-in transition, which happens when the chemical potential mu equals the single soliton energy and temperature is T=0. The soliton density rho _s( mu ,T) and the critical behaviour at T=0 are studied in the classical limit (quantum coupling beta to 0) and in the quantum system with beta ²=4 pi ; the critical exponent for rho _s is 0 and ¹/₂ respectively. An important application of these results is the temperature dependence of an incommensurate charge transfer rho _e in one-dimensional conductors due to Umklapp scattering. rho _e(T) can be determined by the function rho _s( mu ,T).