I have been reading through the nice review Finite temperature properties of doped antiferromagnets by Jaklic and Prelovsek from 2000. They summarise their studies of the t-J model by the Finite temperature Lanczos method.
At first sight the graph below of the temperature and doping dependence of the chemical potential does not look particularly interesting [at least to me]. However, they highlight its significance.
- In a simple Fermi liquid the chemical potential has a positive, quadratic and weak temperature dependence. This is only seen for doping c_h=x=0.3
- For a wide doping range [0.05 < c_h < 0.3] the temperature dependence is approximately linear. The slope changes sign for approximately optimal doping (c_h ~ 0.15).
- The weak temperature dependence for c_h ~ 0.15 means that optimal doping corresponds to maximum entropy! [This can be deduced via the Maxwell relation below. Don't you love thermodynamics!]
- This relation is also related [approximately] to the thermopower via a relationship [equation 8.6], which is essentially a restatement of the Kelvin formula [discussed by Peterson and Shastry].
- The latter means the thermopower should change sign around optimal doping, as is indeed observed [more on that later].
- The large entropy near optimal doping emerges from the interplay of the localised spins [from the remnants of the Mott insulator] and frustration of the antiferromagnetic spin interactions via doping.
I would be interested to see a similar calculation for the Hubbard model on the anisotropic triangular lattice at half filling to see how the chemical potential varies as a function of U/t as the Mott insulator is approached from within the metallic phase.