Momentum-selective metal-insulator transition in the two-dimensional Hubbard model: An 8-site dynamical cluster approximation study

Metal-insulator transitions in the paramagnetic phase of the two-dimensional square-lattice Hubbard model are studied using the dynamical cluster approximation with eight momentum cells. We show that both the interaction-driven and the doping-driven transitions are multistage and momentum-sector specific with Fermi-liquid metal and fully gapped insulator phases separated by an intermediate phase, in which some regions of the Brillouin zone are gapped while others sustain gapless quasiparticles. We argue that this is the coarse-grained version of a gradually shrinking arc or pocket. A pronounced particle-hole asymmetry is found.

Figure 1

(Color online) Left panel: Brillouin zone partitioning associated with the 8-site cluster and definition of the four inequivalent momentum sectors $A$, $B$, $C$, and $D$. The noninteracting Fermi surface for $t^{\prime }=-0.15t$ and density $n=1$ is indicated by the gray line. Right panel: sketch of the paramagnetic-state DCA phase diagram of the Hubbard model on this cluster showing a Fermi-liquid metal phase, an intermediate phase (hashed region), and the insulating state (heavy horizontal line).

Figure 2

(Color online) Sector $B$ (open symbols) and $C$ (filled symbols) Green functions, scaled by the number of equivalent sectors $n_{\alpha }$ and evaluated at the midpoint of the imaginary time interval as a function of $U$ at half filling. The top panel shows results for $t^{\prime }=0$; the bottom panel for $t^{\prime }=-0.15t$.

Figure 3

(Color online) Imaginary part of the self energy in momentum sectors $B$ and $C$ for half filling and $t^{\prime }=0$ $(\beta t=40)$. The interaction strengths are (from top to bottom) $U/t=5$, 5.5, 5.675, 5.75, 5.875, 6, 6.25, 6.375, 6.5, and 6.625.

Figure 4

(Color online) $B$- and $C$-sector dopings (summed over spin and sector degeneracy) as a function of chemical potential for $U/t=7$, $t^{\prime }=0$ at $\beta t=10$, 20, and 40. The doping-driven transition is sector selective with dopants appearing first in the $B$-sector.

Figure 5

(Color online) Main panel: $B$- and $C$-sector dopings (summed over spin and sector degeneracy) and total doping as a function of chemical potential for $U/t=7$, $t^{\prime }=-0.15t$ at $\beta t=20$. Inset: expansion of the electron-doped metal-insulator transition region showing the temperature dependence.

Figure 6

(Color online) Imaginary part of $B$-sector self energies for the doped Hubbard model at $U=7t$, $t^{\prime }=-0.15t$, and $\beta t=20$. Traces indicated by open circles, triangles, and diamonds correspond to $\mu$ where both sector $B$ and sector $C$ are gapped; traces marked by full circles, triangles, and diamonds correspond to $\mu$ where sector $C$ remains undoped and sector $B$ is doped, while traces marked by asterisks, crosses, and plus signs correspond to $\mu$ where both sectors are doped.