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

Abstract

We demonstrate an algebraic construction of frequency-dependent bath orbitals which can be used in a robust and rigorously self-consistent DMFT-like embedding method, here called ω-DMFT, suitable for use with Hamiltonian-based impurity solvers. These bath orbitals are designed to exactly reproduce the hybridization of the impurity to its environment, while allowing for a systematic expansion of this bath space as impurity interactions couple frequency points. In this way, the difficult non-linear fit of bath parameters necessary for many Hamiltonian-formulation impurity solvers in DMFT is avoided, while the introduction of frequency dependence in this bath space is shown to allow for more compact bath sizes. This has significant potential use with a number of new, emerging Hamiltonian solvers which allow for the embedding of large impurity spaces within a DMFT framework. We present results of the ω-DMFT approach for the Hubbard model on the Bethe lattice, a 1D chain, and the 2D square lattice, which show excellent agreement with standard DMFT results, with fewer bath orbitals and more compact support for the hybridization representation in the key impurity model of the method. arXiv:1909.07713v1 [cond-mat.str-el]

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“…5,36 , and for additional work, including some that goes beyond assuming a mean-field Φ, see Refs. 3,[24][25][26][27]29,[45][46][47][48][49] ). The correlation potential u is determined by a self-consistent matching procedure and this is the mathematical problem we seek to address.…”

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“…These were further generalized to provide the derivatives of the Green's function at any frequency in Ref. 31. While these gave compact bath spaces for describing the interacting Green's function of the system, the dynamical nature of the bath introduced additional difficulties.…”

“…This Schmidt decomposition approach to construct bath orbitals has been used before, in the (energyweighted) density-matrix embedding theory [25,26,28,29] and in ω-DMFT [30,31], where the bath states were selected to reproduce (energy weighted) density matrices of the system, or the system single-particle propagator (Green's function) and its derivatives at a given frequency, respectively. Similar decomposition methods have also been used elsewhere, for example in order to automatically partition orbital spaces [32].…”