Effect of on-site hole-phonon (h-ph) interaction within Holstein t-J model has been examined numerically using exact diagonalization (ED) technique within an 8 - site tilted square cluster at a hole doping =0.25. We have applied periodic boundary conditions to obtain the basis states. It appears that with the increase of on-site h-ph interaction λ_1 as well as phonon energy w_0, the ground state energy of the system reduces. Also, the enhancement of the number of phonons results in a significant decrease in ground state energy. At higher temperature, entropy decreases with λ_1 as a result of the formation of S0 bipolarons. Low temperature specific heat indicates non-Fermi liquid behavior of the system.
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