Unconventional metal-insulator transition in two dimensions

We show, by using a correlated Jastrow wave function and a mapping onto a classical model, that the two-dimensional Mott transition in a simple half-filled one-band model can be unconventional and very similar to the binding-unbinding Kosterlitz-Thouless transition of vortices and antivortices, here identified by empty and doubly occupied sites. Within this framework, electrons strongly interact with collective plasmon excitations that induce anomalous critical properties on both sides of the transition. In particular, the insulating phase is characterized by a singular power-law behavior in the photoemission spectrum, which can be continuously connected to the fully projected insulating state relevant to strongly correlated low-energy models.

Figure 1

(Color online) Inverse of the dielectric function $1∕ϵ$ [see Eq. (14)] for the free-electron determinant. Left panel: $1∕ϵ$ as a function of the effective temperature $1∕\beta$ and for different sizes $L$ of the cluster. The critical temperature of the classical Coulomb gas model $T_c^{\mathit{CGM}}$ is marked with a dashed line for a comparison. Right panel: Size scaling of $1∕ϵ$ for various $\beta$.

Figure 2

(Color online) The same as in Fig. 1 but for a gapless BCS state with $\Delta ∕t=1.1$ and $d_{x^2-y^2}$ symmetry.

Figure 3

(Color online) Equal-time density structure factor $N_q$ for the correlated wave function of Eq. (11) (full squares), compared to the same quantity calculated within the Gaussian approximation [indicated as GSA and given by Eq. (15)] (full triangles) for $\beta =4∕\pi$ (upper panel) and $\beta =12∕\pi$ (lower panel; notice the different scale of the GSA data).

Figure 4

(Color online) Quasiparticle weight $Z_k$ at $k=(\pi ∕2,\pi ∕2)$ for the gapless BCS state with $\Delta ∕t=1.1$ and $d_{x^2-y^2}$ symmetry as a function of $L$ and for different Jastrow strengths $\beta$ (full circles). The case of the fully projected wave function (empty circles) is also reported for $\Delta ∕t=1.1$ and 0.5.

Figure 5

(Color online) The behavior of $\theta$ [the exponent of the quasiparticle weight; see Eq. (19)] as a function of $\beta$ for BCS state (full circles) and the Fermi gas (FG) determinant (full squares). The values of the fully projected states are also reported (arrows).

Figure 6

(Color online) Quasiparticle weight $Z_k$ at $k=(\pi ∕2,\pi ∕2)$ of the optimized paramagnetic wave function containing a Jastrow factor applied to the Fermi gas as a function of the interaction $U∕t$ in the Hubbard model, for three different sizes of the system. Inset: The number of double occupancies $D$ as a function of $U∕t$.

Figure 7

(Color online) Optimized Jastrow potential $v_q$, multiplied by ${\mid q\mid }^2$, for the Hubbard model as a function of $\mid q\mid$ [in the (1,1) direction] for different sizes of the cluster and ratios $U∕t$. The arrow indicates $\pi ∕T_c^{\mathit{CGM}}$, the expected value of ${\lim }_{q\to 0}{v}_q{\mid q\mid }^2$ at the classical transition point.