Disorder The Fluctuating Gap Model

This model, which is sometimes referred to as the Fluctuating Gap Model (FGM) [42], has been used to study various aspects of quasi-one-dimensional systems. Examples are the thermodynamic properties of quasi-one-dimensional organic compounds (NMP-TCNQ, TTF-TCNQ) [27], the effect of disorder on the Peierls transition [43, 44], and the effect of quantum lattice fluctuations on the optical spectrum of Peierls materials [41, 45, 46]. 

Here and below we assume s to be positive, which is sufficient in view of the symmetry of p(s) for the Hamiltonian Eq. (3.10). Eor g 2 the density of states has a pseudogap (the Peierls gap filled with disorder-induced states). For g 2 the pseudogap disappears and the density of states becomes divergent at =0. 

From Eq. (3.23) it is clear that at weak disorder (g C 1) the density of states close to the middle of the pseudogap is strongly suppressed. The reason for this is that a large fluctuation of A (x) is required in order to create an electron state with energy Aq. This makes it possible to apply a saddle-point approach to study the typ- 

The saddle-point disorder fluctuation [49-51] (also called the optimal fluctuation) fj x) is the least suppressed one among the required large fluctuations. It can be found by minimizing. 

the soliton-antisoliton separation R is fixed by the condition e+ R)=e. 

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