The strong coupling region

We now turn to the domain / 1. Clearly Eqs. (13.27) are stiO a valid representation of the RG mapping, and the scaling variables still take the form (13.23). However the strong coupling region is not connected to a 0- 

Since —. 472 we conclude that the leading corrections to fixed point behavior in the strong coupling regime as described by our theory are proportional to and thus dominate the nonuniversal corrections 

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Fig. 13.2. Crossover diagram in the w — / plane (uncritical surface). The shaded parts indicate regions dominated by asymptotic power law behavior. Weak coupling region (/ < 1) Long dashes lines of fixed z (— 300 1, from above). Short dashes lines of fixed sfz (= 0,01 1, from above). Dotted lines of fixed s = (0-02 0,8, from above). In the strong coupling region a line of fixed z = 300 is shown...

In the strong-coupling region, the SDW response dominates, as expected from the result of 5 = 1 for the first-excited state (see Fig. 9). The decrease of the SCPO and SCPl responses can be understand in terms of the Lehmann representation of /P as... 

Let us start with ht A a Holstein model. In the strong-coupling region, it is usually the case to employ the Lang-Firsov transformation [80], defined as... 

Here in the strong coupling region, it is apparent that the magnitude of the displacement in the CT state can significantly affect the observed value of S. We note that in the adiabatic limit, the vibrational wavefunctions are anharmonic. However, for small vibrational quantum numbers, the wavefunctions can be approximated by linearly displaced oscillators with renormalized temperature dependent frequencies and displacements. A large S in the CT state can now appear to substantially increase the observed S value in the P band. 

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