Local moments and magnetic order in the two-dimensional Anderson-Mott transition

We study the role of electronic correlation in a disordered two-dimensional model by using a variational wave function that can interpolate between Anderson and Mott insulators. Within this approach, the Anderson-Mott transition can be described both in the paramagnetic sector and in the magnetic sector. In the latter case, we find evidence for the formation of local magnetic moments that order before the Mott transition. The charge gap opening in the Mott insulator is accompanied by the vanishing of the ${\text{lim}}_{q\to 0}\overline{⟨n_q⟩⟨n_{-q}⟩}$ (the bar denoting the impurity average). The role of a frustrating (second-neighbor) hopping is also discussed, with a particular emphasis to the formation of metastable spin-glass states.

Figure 1

(Color online) (a) Connected term of the density-density correlation function $N_q^{\text{conn}}$ divided by $\left|q\right|$. (b) Jastrow parameters $v_q$ multiplied by ${\left|q\right|}^2$. (c) Disconnected term of the density-density correlation function $N_q^{\text{disc}}$ as a function of $U$. (d) Fluctuations of the on-site variational energies ${\Delta }_{ϵ}$ and of the local densities. All calculations have been done for $D/t=5$.

Figure 2

(Color online) Staggered magnetization $M$ for $Q=\left(\pi ,\pi \right)$ and compressibility fluctuations $N_q^{\text{disc}}$ as a function of $U$ for disorder $D/t=5$ (upper panel) and as a function of $D$ for $U/t=4$ (bottom panel). In the bottom panel, we also report the results of $M$ for the unprojected wave function $|{\Phi }_0⟩$ (upper curve). Fluctuations of the on-site variational energies ${\Delta }_{ϵ}$ and of the local densities (middle panel). Calculations have been done for $N=98$ and error bars indicate the average over different realizations of disorder.

Figure 3

Local density $⟨n_i⟩$ (upper panels) and local magnetization $⟨m_i⟩$ (lower panels) for a given disorder realization with $D/t=5$ and different values of $U/t$. The black contour shows the elementary cell of the lattice which is repeated to mimic the infinite lattice with periodic boundary conditions.

Figure 4

Local magnetization $⟨m_i⟩$ for the best variational state (lower panels) and for a metastable solution (upper panels) for a given disorder configuration with $D/t=5$ and $t^{\prime }/t=1$.