Charge and spin criticality for the continuous Mott transition in a two-dimensional organic conductor

We study the continuous bandwidth-controlled Mott transition in the two-dimensional single-band Hubbard model with a focus on the critical scaling behavior of charge and spin degrees of freedom. Using plaquette cluster dynamical mean-field theory, we find charge and spin criticality consistent with experimental results for organic conductors. In particular, the charge degree of freedom calculated via the local density of states at the Fermi level shows a smoother transition than expected for the Ising universality class and in single-site dynamical mean-field theory, revealing the importance of short-ranged nonlocal correlations in two spatial dimensions. The spin criticality obtained from the local spin susceptibility agrees quantitatively with nuclear magnetic resonance measurements of the spin-lattice relaxation rate.

Figure 1

Schematic path through the continuous Mott transition at fixed temperature. We assume that the pressure-controlled transition in Ref.7 corresponds approximately to the bandwidth-controlled transition in the Hubbard model. The hopping amplitude $t$ (bandwidth $W\propto t$) is varied (blue arrow) while the local Coulombic repulsion $U$, the relative anisotropic diagonal hopping $t_{\text{diag}}/t$, and the temperature $T$ are kept fixed in our calculations. The indicated values of ${(T/U)}_c$ and ${(t/T)}_c$ are the critical values found for $t_{\text{diag}}/t=0.44$.

Figure 2

Critical behavior at the continuous bandwidth-controlled Mott transition (vertical dashed line, ${(T/t)}_c=7.68$). Upper panel: Evolution of $({\sigma }_{\mathrm{ch}}-{\sigma }_{c,\mathrm{ch}})/{\sigma }_{c,\mathrm{ch}}$ and $({\sigma }_{sp}-{\sigma }_{c,sp})/{\sigma }_{c,sp}$ upon increasing $t/T$. The solid curves are fits to the critical scaling behavior for the exponent $\delta$ according to Eq. (1). Lower panel: Double-logarithmic plot of the same data measured from the critical end point of the Mott transition. Solid lines show the scaling fits (the same fits as in the upper panel). Error bars are estimated from the linear regression fit to the data in the double-logarithmic scale.