Effect of quantum lattice fluctuations on the dimerized ground state of the Takayama-Lin-Liu-Maki model

The effect of quantum lattice fluctuations on the dimerized ground state is studied in the half-filled-band Takayama-Lin-Liu-Maki model. The nonadiabatic effect due to finite phonon frequency (Formula presented)≳0 is treated through an energy-dependent electron-phonon scattering function δ((Formula presented), k) introduced by means of a unitary transformation. This leads to a weakening of the effective (adiabatic) potential stabilizing the dimerized state and results in four-fermion interaction. By decoupling of the electronic correlations we show that our approach gives a good description of the continuous variation of the dimerization as functions of the dimensionless coupling constant (Formula presented) and the phonon frequency (Formula presented) when the ratio (Formula presented)/πt (t is the electron hopping integral) is not large. Our results show that, at least in the weak-coupling limit, quantum lattice fluctuations change the functional dependence of the dimerization parameter (Formula presented) on the coupling constant even if the ratio (Formula presented)/πt is small (but finite). In the spin-1/2 case our result is the same as that predicted by Fradkin and Hirsch. But in the spinless case we still predict a long-range dimerization order even if the coupling is weak and (Formula presented)/πt is finite. In the large (Formula presented) (antiadiabatic) limit we show that our effective Hamiltonian becomes an n-component Gross-Neveu model and the ratio (Formula presented)((Formula presented)=∞)/(Formula presented)((Formula presented)=0) is equal to 1/cosh(π/2(Formula presented)) (n=1: spinless; n=2: spin-1/2). By using the same input parameters as those of some previous authors we get a 7.2% reduction of the dimerization parameter (Formula presented) compared with the adiabatic value.