Augmented hybrid exact-diagonalization solver for dynamical mean field theory

We present a methodology to solve the Anderson impurity model in the context of dynamical mean field theory based on the exact-diagonalization method. We propose a strategy to effectively refine the exact-diagonalization solver by combining a finite-temperature Lanczos algorithm with an adapted version of the cluster perturbation theory. We show that the augmented diagonalization yields an improved accuracy in the description of the spectral function of the single-band Hubbard model and is a reliable approach for a full $d$-orbital manifold calculation.

Figure 1

Sketch of the AIM in ED-CPT: the impurity (center circle) is connected to $N_b$ nearest-neighbor bath sites (stars), and each of the latter is connected by a small perturbative parameter $V_{\mathrm{CPT}}$ to a line of additional sites (squares, $N_c$ sites in each chain). The sites within each chain are connected together with both nearest and long-range hoppings. The inner system (light filling) is solved by using a standard Lanczos algorithm. The Green's function of the full system (inner and outer region) is obtained by treating the full system by cluster perturbation theory.

Figure 2

Spectral function $\rho \left(\omega \right)$ obtained for the Hubbard model solved by ED-CPT at (a) $U/D=1.5$ and (c) $U/D=4$. For comparison, the spectral functions obtained by ED at (b) $U/D=1.5$ and (d) $U/D=4$ are shown. The ED results with $N_b=3$ (diamonds) and $N_b=7$ (squares) bath sites are compared with the DMRG results (circles). The CPT-ED results obtained with $N_b=3$ inner bath sites and augmented with lines of $N_c=6$ sites (diamonds) and, respectively, $N_b=7$ and $N_c=4$ (squares) compare remarkably well to the DMRG data (circles).

Figure 3

(a) Fitting distance $d$ obtained by using the ED and ED-CPT. (b) Integrated absolute value of the difference in the spectral functions for the Hubbard model with $U/D=1.5$.

Figure 4

Imaginary-frequency Green's function: Real (a,b) and imaginary part (c,d) of the Green's function $\mathbf{G}$ for a multiorbital system (paramagnetic VO${}_2$). The data obtained by (a,c) ED-CPT (filled symbols) and (b,d) by ED (filled symbols) are compared with reference data obtained by CTQMC (open symbols) reproduced from Ref. 22. The calculations include all five $d$ orbitals ($e_g$ and $t_{2g}$).