Ground state of the lattice model

By averaging // = /7L + /7T (equations (6) and (7)) over the phonon wave functions (9) with equation (10) one obtains for the site Hamiltonian (6) the local part in the form 

Expressions Et (equation (20)) in the ground state are independent of q and n because of the form of yiq(ri) = y, exp(—iqna) (14). This substantially simplifies subsequent calculations leaving Is, and Cj as functions of yf independent on n. The transfer terms 77Ti, i = 1, 2, 3, 4 in equation (18) with equation (19) are 

The effective polaron potential in equation (15) (with equations (16)-(20)) as a highly nonlinear function of y1 and y2 is visualized in Fig. 1. 

The potential exhibits two sets of minima related to two competing ground states  

The ground state energies related to these two sets of competing minima were calculated numerically. The result of the numerical minimalization of the 

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