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arXiv:2503.09881

New perspectives on Density-Matrix Embedding Theory

Alicia Negre, Fabian M. Faulstich, Raehyun Kim, Thomas Ayral, Lin Lin, Eric Cancès B

Published Mar 12, 2025• 0 citations

Abstract

Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these, Density Matrix Embedding Theory (DMET) is an efficient approach that enforces self-consistency at the level of one-particle reduced density matrices (1-RDMs), facilitating applications across diverse quantum systems. However, conventional DMET is constrained by the requirement that the global 1-RDM (low-level descriptor) be an orthogonal projector, limiting flexibility in bath construction and potentially impeding accuracy in strongly correlated regimes. In this work, we introduce a generalized DMET framework in which the low-level descriptor can be an arbitrary 1-RDM and the bath construction is based on optimizing a quantitative criterion related to the maximal disentanglement between different fragments. This yields an alternative yet controllable bath space construction for generic 1-RDMs, lifting a key limitation of conventional DMET. We demonstrate its consistency with conventional DMET in appropriate limits and exploring its implications for bath construction, downfolding (impurity Hamiltonian construction), low-level solvers, and adaptive fragmentation. We expect that this more flexible framework, which leads to several new variants of DMET, can improve the robustness and accuracy of DMET.

DOI: 10.48550/arxiv.2503.09881

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\mathrm{impurity}+\mathrm{bath}

'' cluster's Hamiltonian (from which approximate local properties of the interacting lattice can be extracted) becomes an explicit functional of the density matrix. In the spirit of single-impurity DMET, we consider in this work a closed (two-electron) cluster constructed from the full-size noninteracting density matrix. When the (Householder-transformed) interaction on the bath site is taken into account, per-site energies obtained for the half-filled one-dimensional Hubbard lattice match almost perfectly the exact Bethe ansatz results in all correlation regimes. In the strongly correlated regime, the results deteriorate away from half-filling. This can be related to the electron number fluctuations in the (two-site) cluster which are neither described in Ht-DMFET nor in regular DMET. As expected, the per-site energies dramatically improve when increasing the number of embedded impurities. Formal connections with density/density matrix functional theories have been briefly discussed and should be explored further. Work is currently in progress in this direction.

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