Rigorous wave function embedding with dynamical fluctuations

Abstract

The dynamical fluctuations in approaches such as dynamical mean-field theory (DMFT) allow for the self-consistent optimization of a local fragment, hybridized with a true correlated environment. We show that these correlated environmental fluctuations can instead be efficiently captured in a wave function perspective in a computationally cheap, frequency-independent, zero-temperature approach. This allows for a systematically improvable, short-time wave function analogue to DMFT, which entails a number of computational and numerical benefits. We demonstrate this approach to solve the correlated dynamics of the paradigmatic Bethe lattice Hubbard model, as well as detailing cluster extensions in the one-dimensional Hubbard chain where we clearly show the benefits of this rapidly convergent description of correlated environmental fluctuations. arXiv:1808.09321v4 [cond-mat.str-el]

Frequency-dependent and algebraic bath states for a dynamical mean-field theory with compact support

“…12 and 13. 24 Since the moments relate directly to the high frequency expansion of the Green's function (z − h Weiss ) −1 , adding static bath orbitals corresponding to higher moments can be seen as a systematic expansion of the Green's function in the high-frequency limit, though the fact that particle and hole moments are separately matched means that this is not purely a high-energy expansion.…”

“…4. For each cluster κ, solve the ground-state equation (24) with ED and the response equations (25,26). From the ground and response states, construct the impurity Green's function (27) and the new impurity self-energy via the Dyson equation (28).…”

Energy-weighted density matrix embedding of open correlated chemical fragments

“…However, since the two-body interactions in the correlated Hamiltonian cause splittings of the hole and particle states, the number of many-body states which are summed over to construct the correlated EwRDMs is exponentially larger than in the single-particle case. The aim of the approach described here (EwDMET) 28 , is to self-consistently match the matricesT (n) h/p = T (n) h/p spanning a correlated fragment of the molecule, for all EwRDMs up to a given order, denoted by n mom . The quantities in Eqs.…”

“…Upon extension of the Fock matrix with the additional degrees of freedom, the total number of electrons also needs to be augmented to match the moments. In our previous work 28 this was achieved by working in a grand canonical ensemble, with a fictitious (low) temperature, with the total electron filling smoothly changed via the chemical potential. However, in this work we work at zero temperature with a fixed integer filling of the orbitals.…”

“…Very recently, the authors presented an alternative approach, which formally overcomes the limitations of the DMET method, dubbed 'Energy-weighted Density Matrix Embedding Theory' (EwDMET) 28 . This allows for a systematically improvable and self-consistent description of the missing correlated (one-particle) quantum fluctuations from the fragment into the environment, in a rigorously selfconsistent fashion.…”