Bath parameterization in multi-band cluster Dynamical Mean-Field Theory

TL;DR

This work systematically probes how bath discretization affects Hamiltonian-based CDMFT solutions for 1- and 2-band Hubbard models by employing ASCI to access larger impurity baths. It contrasts three bath parameterizations—SDR, Irreps, and Symmetry-preserving Replicas—and analyzes their impact on convergence, nonlocal correlations, and the zero-temperature Mott transition. For the single-band case, results converge across parameterizations with sufficiently large baths, while small baths can yield nematic tendencies or parameterization-dependent transition features; in the two-band case, some parameterization dependence persists even at larger baths, underscoring the challenge of multi-orbital embedding. Overall, the study highlights the necessity of systematic bath-size convergence and provides a robust framework (CDMFT+ASCI) for exploring strong correlations in complex materials where conventional ED is prohibitive.

Abstract

Accurate and reliable algorithms to solve complex impurity problems are instrumental to a routine use of quantum embedding methods for material discovery. In this context, we employ an efficient selected configuration interaction impurity solver to investigate the role of bath discretization, specifically, bath size and parameterization, in Hamiltonian-based cluster dynamical mean field theory (CDMFT) for the one- and two-orbital Hubbard models. We consider two- and four-site clusters for the single-orbital model and a two-site cluster for the two-orbital model. Our results demonstrate that, for small bath sizes, the choice of parameterization can significantly influence the solution, highlighting the importance of systematic convergence checks. Comparing different bath parameterizations not only reveals the robustness of a given solution but can also provide insights into the nature of different solutions and potential instabilities of the paramagnetic state. We present an extensive analysis of the zero-temperature Mott transition of the paramagnetic half-filled single-band Hubbard model, benchmarking our findings against previous literature. We find that for the single-band model the dependence on parameterization is weak for the largest bath sizes accessible with ASCI, while a tendency towards a nematic solution can be seen when the bath size is small. Building on this, we extend our study to the multi-band regime, where we present the first systematic analysis at zero temperature for two orbitals and a two-site cluster. This setup allows us to assess the effect of nearest-neighbor dynamical correlations on the multi-orbital Mott transition. In this case, some quantitative dependence on the parameterization is retained for the two-orbital model, for instance in the value of the critical interaction for a Mott transition.

Figures (10)

• Figure 1: Visual representation of the different bath parameterizations in the $1\times 2$ impurity cluster for the single band Hubbard model. Here, different colors for the couplings or the bath sites indicate independent degrees of freedom. The most general bath parameterization would require $6N_{\text{sets}}$ degrees of freedom, where $N_{\text{sets}}=N_b/N_C$.
• Figure 2: Cluster quantities of the $1\times 2$ CDMFT solutions of the half-filled single band Hubbard model as a function of the interaction strength. Left: Quasiparticle residue of the impurity, spectral weight at low frequency in the local spectral function, and real part of the off-diagonal self energy at zero frequency. Right: Double occupancy, local and nearest neighbor spin-spin correlations.
• Figure 3: Cluster quantities of the $2\times 2$ CDMFT solutions of the half-filled single band Hubbard model as a function of the interaction strength. Left: Quasiparticle residue of the impurity, spectral weight at low frequency in the local spectral function, real part of the off-diagonal self energy at zero frequency and nematic order parameter. Right: double occupancy, local, next-nearest neighbor and nearest neighbor spin-spin correlations.
• Figure 4: Comparison of our results for the double occupancies in the cluster sites with references zhang_pseudogap_2007 and balzer_first-order_2009 for the half-filled single band Hubbard model solved with a $2\times2$ impurity cluster.
• Figure 5: Evolution of the density of states with increasing interaction strength in (a) the $N_{b}=8$ solution and (b) the $N_{b}=16$ solution. The dotted lines show the integration limits $\left[-\frac{t}{2},\frac{t}{2}\right]$ for the estimation of spectral weight at low frequency.