Figure 1

Dynamical mean-field theory. (a) DMFT neglects spatial fluctuations around a single lattice site j and replaces the rest of the lattice with an effective mean-field \(\Delta(\tau-\tau')\) with which the isolated site dynamically exchanges fermions, subject to the self-consistency condition \(G^{R}_{\mathrm{imp}}(\omega)= G^{R}_{{\mathrm{latt}},jj}(\omega)\). Here, \(G^{R}_{\mathrm{imp}}(\omega)\) is the impurity Green function and \(G^{R}_{{\mathrm{latt}},jj}(\omega)\) is the local part of the lattice Green function. (b) In Hamiltonian-based DMFT methods, one considers an impurity model which describes the local part of the Hubbard model directly and represents the mean-field as a set of non-interacting bath sites that are connected to the central, interacting impurity site. (c) The minimal representation of DMFT involves the impurity site, with on-site interaction U and chemical potential μ, coupled via the hybridization energy V to only one bath site. The bath has on-site energy \(\epsilon_{c}\) that corresponds to the mean-field \(\Delta(\tau-\tau')\) and is subject to two self-consistency conditions.