Extending density matrix embedding: A static two-particle theory

Charles J. C. Scott and George H. Booth

Phys. Rev. B 104, 245114 – Published 9 December 2021

Abstract

We introduce extended density matrix embedding theory (EDMET), a static quantum embedding theory explicitly self-consistent with respect to local two-body physics. This overcomes the biggest practical and conceptual limitation of more traditional one-body embedding methods, namely the lack of screening and treatment of longer-range interactions. This algebraic zero-temperature embedding augments a local interacting cluster model with a minimal number of bosons from a description of the full system correlations via the random phase approximation, and admits an analytic approach to build a self-consistent Coulomb-exchange-correlation kernel. For extended Hubbard models with nonlocal interactions, this leads to the accurate description of phase transitions, static quantities, and dynamics. We also move towards ab initio systems via the Parriser-Parr-Pople model of conjugated coronene derivatives, finding good agreement with experimental optical gaps.

Received 9 July 2021
Revised 28 October 2021
Accepted 29 November 2021

DOI:https://doi.org/10.1103/PhysRevB.104.245114

Physics Subject Headings (PhySH)

Strongly correlated systems

Diagrammatic methods Electron-correlation calculations Electronic structure Extended Hubbard model Random phase approximation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Charles J. C. Scott ^* and George H. Booth ^†

Department of Physics, King's College London, The Strand, London WC2R 2LS, United Kingdom

^*cjcargillscott@gmail.com
^†george.booth@kcl.ac.uk

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Issue

Vol. 104, Iss. 24 — 15 December 2021

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Images

Figure 1
Phase diagram of the 1D extended Hubbard model (left), with charge-density wave (CDW), spin-density wave (SDW), and paramagnetic (PM) regions of the parameter space. The white region indicates a stable coexistence of CDW and SDW phases for this choice of lattice and fragment size, with the dotted line indicating the lowest value of $V / t$ at which CDW becomes energetically favored, indicating the relative energetic stability of the phase. (Right) Double occupancy of antiferromagnetic (AFM) and charge ordered (CO) extended-DMET (EDMET) solutions, averaged over the two fragment sites at $U / t = 6$ , showing the coexistence and phase transition behavior between the regions.
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Figure 2
EDMET spectra of (a) the dynamical spin structure factor and (b) the renormalized charge structure factor of the 50-site extended Hubbard model with $U / t = 7.8$ and $V = 1.3 t$ . A broadening of $0.25 t$ was used.
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Figure 3
Spectral functions of the dynamical spin structure factor and renormalized charge structure factor for the 50-site extended Hubbard model at half-filling with $U / t = 7.8$ and $V = 1.3 t$ calculated via (a) RPA upon an unrestricted HF calculation, and (b) RPA upon a converged DMET mean-field state, where the bare Coulomb interaction is used. A finite broadening of $0.25 t$ was used in all cases. Note that the scale is different to Fig. 2.
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Figure 4
Modifications to the two-point component of the interaction (Coulomb-exchange-correlation) kernel in the lattice of the EDMET due to the self-consistency ( $Δ {\tilde{K}}_{p p q q} = K - v$ ) on a symlog scale. This demonstrates the renormalization of the effective interaction to account for fragment exchange and correlation effects, and is used in the resulting RPA. These are obtained in the half-filled 32-site 1D extended Hubbard model, with (a) $U / t = 7.8$ and $V / t = 1.3$ , or (b) $V / t = 5$ . Even (odd) spin-orbital indices correspond to $α$ ( $β$ ) spin states along the chain.
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Figure 5
The phase transition in the $6 \times 6$ 2D extended Hubbard model, showing the charge versus spin order of the lowest energy stable phase, defined over a $2 \times 2$ plaquette built from coupled two-site fragments.
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Figure 6
Structures and fragmentations of the coronene derivatives treated in this work. Solid lines indicate nearest neighbors, while red dotted lines indicate the specific fragmentation of the lattice chosen. All two-site clusters were solved separately and self-consistently coupled, with no symmetries exploited.
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