Dynamical Mean Field Theory with the Density Matrix Renormalization Group

A new numerical method for the solution of the dynamical mean field theory’s self-consistent equations is introduced. The method uses the density matrix renormalization group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized.

Figure 1

Half-filled Hubbard model density of states ($\frac{1}{\pi }\mathrm{I}\mathrm{m}G(\omega )$) [25] pinning.

Figure 2

Imaginary part of the Green functions at imaginary (Matsubara) frequencies (solid lines). We also show quantum Monte Carlo results (circles) at low temperature $T=1/32$.

Figure 3

DOS at the Fermi energy (squares) and gap (circles) for (a) $U=2.3$ and (b) $U=2.5$. Open (closed) symbols correspond to metallic (insulating) solutions. The thick arrow shows the critical length ($L_c$) above which a metallic solution is obtained. (c) Gap (circles) and inverse of the second moment of the DOS (diamond) as a function of $U$. The values correspond to extrapolations to infinite-size chains. (d) $1/L_c$ as a function of $U$.

Figure 4

Density of states for $U=2.5$ (solid line). For comparison NRG (dot-dashed line) and IPT (dashed line) results are also shown. (a) Insulating solution. (b) Metallic solution.