Thermodynamic Properties of the Planart−JModel

Several thermodynamic quantities within the planar $t-J$ model are calculated using the $T>\mathrm{}0\mathrm{}$ Lanczos method on clusters of up to 26 sites. The hole density $c_h(\mu ,T)$ shows a non-Fermi-liquid behavior as a function of $T$ and suggests a transition from small to large Fermi surfaces at $c_h\sim 0.15$. The specific heat reveals a maximum at the exchange energy scale up to $c_h=0.2\mathrm{}$, where it becomes almost $T$ independent for $T\gtrsim 0.15t$. At constant $T$ the entropy has maximum for $c_h\sim 0.15$ with large values at low $T$, consistent with experiments on cuprates. In the underdoped regime the spin susceptibility ${\chi }_0\left(T\right)$ exhibits a maximum at finite ${T=T}^{*}$, with $T^{*}$ decreasing with doping and disappearing for $c_h>0.15\mathrm{}$.