Finite Doping Signatures of the Mott Transition in the Two-Dimensional Hubbard Model

Experiments on layered materials call for a study of the influence of short-range spin correlations on the Mott transition. To this end, we solve the cellular dynamical mean-field equations for the Hubbard model on a plaquette with continuous-time quantum Monte Carlo calculations. The normal-state phase diagram as a function of temperature $T$, interaction strength $U$, and filling $n$ reveals that upon increasing $n$ towards the insulator, there is a surface of first-order transition between two metals at nonzero doping. For $T$ above the critical end line there is a maximum in scattering rate.

Figure 1

(a) Chemical potential-interaction-temperature phase diagram of the two-dimensional Hubbard model obtained by cellular DMFT. Cross sections at constant $U$ are shown. Dark gray (blue) shaded regions represent the coexistence of two phases. Light gray (yellow) areas denote the onset of the Mott insulator state, characterized by a total occupation $n=1$. Projections on $\mu =0$ and $T=0$ planes are also shown (full lines and dashed lines, respectively). Open dots mark the extrapolated $T=0$ values of $U_{c1}$ and $U_{c2}$. A critical end line (dotted line) begins at the full dot $U_{\mathrm{MIT}}$. (b)–(e) The cross sections at constant $U$ are shown in several $T\mathrm{\text{−}}\mu$ plots. Three phases can be distinguished: metal (open circles), Mott insulator (crosses), momentum selective phase where some regions of the Brillouin zone are gapped and others gapless (filled squares).

Figure 2

Occupation $n$ vs $\mu$ for different values of interaction strength $U$. The data shown are for temperatures $T/t=1/10,1/25,1/50$ (triangles, squares, and circles, respectively). When two solutions are found to coexist, the solutions obtained following the metallic and the insulating solution are indicated as full and open symbols, respectively. The plateau in the occupation at $n=1$ signals the onset of the incompressible Mott state.

Figure 3

(a)–(d) Statistical weight $P$ of the following cluster eigenstates as a function of $\mu$, for several values of $U$, and at the low temperature $T/t=1/50$: the singlet $|N=4,S=0,K=(0,0)⟩$, triplet $|N=4,S=1,K=(\pi ,\pi )⟩$, and doublet $|N=3,S=1/2,K=(\pi ,0)⟩$ (squares, triangles, and circles, respectively), where $N$, $S$, and $K$ are the number of electrons, the total spin, and the cluster momentum of the cluster eigenstate. (e)–(h) Scattering rate $\Gamma =-\mathrm{Im}{\Sigma }_{(\pi ,0)}(\omega \to 0)$ in the sector $(\pi ,0)$ vs $\mu$, at $T/t=1/50$.