The Figure below shows the phase diagram of the Hubbard model on the anisotropic triangular lattice at half filling.as a function of temperature and t/U obtained from cluster DMFT. The figure is taken from this PRB by Liebsch, Ishida, and Merino.
As U/t increases there is a first order phase transition from a metallic to and Mott insulating phase. This first order line ends at a critical point.
(a) and (b) are for t'/t=0.8 and 1, respectively.
Note that the slope of the line at low temperatures depends on the ratio t'/t, reflecting the effect of frustration.
The Clausius-Clapeyron equation and the positive slope of the phase boundary implies that for t'=t that the insulating state has a larger entropy than the metallic state, even at low temperatures. The calculated diagram for t'=0.8t is in semi-quantitative agreement with the observed temperature-pressure phase diagram of a range of organic charge transfer salts. The diagram for t'=t is consistent with that observed for kappa-(ET)2(CN)3, which may have a spin liquid ground state.
The calculated values of the critical temperature Tc = 40-50 K, at which the first order line terminates, are comparable to experimental values.
Furthermore, the Figure shows how frustation can produce a Mott insulating state in which the entropy at low temperatures is larger than that of the metallic state. Such a large entropy is characteristic of a spin liquid.
This leads to a first-order phase boundary which has a positive slope.
In contrast, in a two-dimensional antiferromagnetic Heisenberg model on the square lattice [which have a Neel ordered ground state] at low temperatures has an entropy that is proportional to T^2. At low enough temperature this will always be less than the entropy of a Fermi liquid which is proportional to temperature.
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