Multichain Approach to the Single-Impurity Anderson Model in the Dynamical Mean-Field Theory

Anna Kauch, Krzysztof Byczuk

Claas Grenzebach, G. Czycholl

Ping Sun, Gabriel Kotliar

Daniel Ruhl, Florian Gebhard

We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe lattice with an infinite coordination number up to and including third order in the inverse Hubbard interaction. We employ the Kato-Takahashi perturbation theory to solve the self-consistency equation of the dynamical mean-field theory analytically for the single-impurity Anderson model in multichain geometry. The weight of the secondary Hubbard sub-bands is of fourth order so that the two-chain geometry is sufficient for our study. Our results for the Mott-Hubbard gap and the density of states of the lower Hubbard band agree very well with those from numerical dynamical density-matrix renormalization group calculations, apart from a resonance contribution at the upper band edge, which cannot be reproduced in low-order perturbation theory.

Christian Gramsch, Karsten Balzer, Martin Eckstein +1 more

We derive an exact mapping from the action of nonequilibrium dynamical mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with time-dependent parameters, which can be solved numerically by exact diagonalization. The representability of the nonequilibrium DMFT action by a SIAM is established as a rather general property of nonequilibrium Green functions. We also obtain the nonequilibrium DMFT equations using the cavity method alone. We show how to numerically obtain the SIAM parameters using Cholesky or eigenvector matrix decompositions. As an application, we use a Krylov-based time propagation method to investigate the Hubbard model in which the hopping is switched on, starting from the atomic limit. Possible future developments are discussed.

Karsten Balzer, Zheng Li, Oriol Vendrell +1 more

Nonequilibrium dynamical mean-field theory (DMFT) solves correlated lattice models by obtaining their local correlation functions from an effective model consisting of a single impurity in a self-consistently determined bath. The recently developed mapping of this impurity problem from the Keldysh time contour onto a time-dependent single-impurity Anderson model (SIAM) [C. Gramsch et al., Phys. Rev. B 88, 235106 (2013)] allows one to use wave-function-based methods in the context of nonequilibrium DMFT. Within this mapping, long times in the DMFT simulation become accessible by an increasing number of bath orbitals, which requires efficient representations of the time-dependent SIAM wave function. These can be achieved by the multiconfiguration time-dependent Hartree (MCTDH) method and its multilayer extensions. We find that MCTDH outperforms exact diagonalization for large baths in which the latter approach is still within reach and allows for the calculation of SIAMs beyond the system size accessible by exact diagonalization. Moreover, we illustrate the computation of the self-consistent two-time impurity Green's function within the MCTDH second quantization representation.