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

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Abstract
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).