We analyze the transformation from insulator to metal induced by thermal fluctuations within the Falicov-Kimball model. Using the dynamic mean field theory (DMFT) formalism on the Bethe lattice we find rigorously the temperature dependent density of states (DOS) at half filling in the limit of high dimensions. At zero temperature ($T=0$) the system is ordered to form the checkerboard pattern and the DOS has the gap $\Delta$ at the Fermi level ${\varepsilon }_F=0$, which is proportional to the interaction constant $U$. With an increase of $T$ the DOS evolves in various ways that depend on $U$. For $U>U_{cr}$ the gap persists for any $T$ (then $\Delta >0$), so the system is always an insulator. However, if $U<U_{cr}$, two additional subbands develop inside the gap. They become wider with increasing $T$ and at a certain $U$-dependent temperature $T_{\mathrm{MI}}$ they join with each other at ${\varepsilon }_F$. Since above $T_{\mathrm{MI}}$ the DOS is positive at ${\varepsilon }_F$, we interpret $T_{\mathrm{MI}}$ as the transformation temperature from insulator to metal. It appears that $T_{\mathrm{MI}}$ approaches the order-disorder phase transition temperature $T_{\mathrm{O}\text{−}\mathrm{DO}}$ when $U$ is close to 0 or $U_{cr}$, but $T_{\mathrm{MI}}$ is substantially lower than $T_{\mathrm{O}\text{−}\mathrm{DO}}$ for intermediate values of $U$. Moreover, using an analytical formula we show that $T_{\mathrm{MI}}=0$ at $U=\sqrt{2}<U_{cr}$, so we prove that the quantum critical point exists for the ordered metal at $(T=0,U=\sqrt{2})$. Having calculated the temperature dependent DOS we study thermodynamic properties of the system starting from its free energy $F$. Then we find how the order parameter $d$ and the gap $\Delta$ change with $T$ and we construct the phase diagram in the variables $T$ and $U$, where we display regions of stability of four different phases: ordered insulator, ordered metal, disordered insulator, and disordered metal. Finally, we use a low temperature expansion to demonstrate the existence of a nonzero DOS at a characteristic value of $U$ on a general bipartite lattice.

• Received 3 October 2013

DOI:https://doi.org/10.1103/PhysRevB.89.075104