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Using the example of the sawtooth chain, we argue that the t-J model sharesimportant features with the Hubbard model on highly frustrated lattices. Thelowest single-fermion band is completely flat (for a specific choice of thehopping parameters $t_{i,j}$ in the case of the sawtooth chain), giving rise tosingle-particle excitations which can be localized in real space. Theselocalized excitations do not interact for sufficient spatial separations suchthat exact many-electron states can also be constructed. Furthermore, all theseexcitations acquire zero energy for a suitable choice of the chemical potential$\mu$. This leads to: (i) a jump in the particle density at zero temperature,(ii) a finite zero-temperature entropy, (iii) a ferromagnetic ground state witha charge gap when the flat band is fully occupied and (iv) unusually largetemperature variations when $\mu$ is varied adiabatically at finitetemperature.

Enhanced low-temperature entropy and flat-band ferromagnetism in the t-J model on the sawtooth lattice