Fully Algebraic and Self-consistent Effective Dynamics in a Static Quantum Embedding

TL;DR

This paper introduces a fully algebraic, self-consistent static quantum embedding method that converges systematically to dynamical mean-field theory, avoiding numerical fitting and enabling analysis of correlated quantum systems.

Contribution

The authors reformulate EwDMET to be equivalent to an optimal truncation of DMFT dynamics, providing an analytic, self-consistent approach that converges to DMFT without numerical fitting.

Findings

Successfully applied to Bethe lattice Hubbard model in infinite dimensions.

Demonstrates rapid convergence for 1D and 2D Hubbard models.

Enables calculation of Fermi liquid parameters and renormalized dynamics.

Abstract

Quantum embedding approaches involve the self-consistent optimization of a local fragment of a strongly correlated system, entangled with the wider environment. The `energy-weighted' density matrix embedding theory (EwDMET) was established recently as a way to systematically control the resolution of the fragment-environment coupling, and allow for true quantum fluctuations over this boundary to be self-consistently optimized within a fully static framework. In this work, we reformulate the algorithm to ensure that EwDMET can be considered equivalent to an optimal and rigorous truncation of the self-consistent dynamics of dynamical mean-field theory (DMFT). A practical limitation of these quantum embedding approaches is often a numerical fitting of a self-consistent object defining the quantum effects. However, we show here that in this formulation, all numerical fitting steps can be entirely circumvented, via an effective Dyson equation in the space of truncated dynamics. This provides a robust and analytic self-consistency for the method, and an ability to systematically and rigorously converge to DMFT from a static, wave function perspective. We demonstrate that this improved approach can solve the correlated dynamics and phase transitions of the Bethe lattice Hubbard model in infinite dimensions, as well as one- and two-dimensional Hubbard models where we clearly show the benefits of this rapidly convergent basis for correlation-driven fluctuations. This systematically truncated description of the effective dynamics of the problem also allows access to quantities such as Fermi liquid parameters and renormalized dynamics, and demonstrates a numerically efficient, systematic convergence to the zero-temperature dynamical mean-field theory limit.