Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1812.07027 · Physical review. B./Physical review. B

Effect of propagator renormalization on the band gap of insulating solids

Sergei Iskakov, Alexander A. Rusakov, Dominika Zgid, Emanuel Gull

Published Aug 5, 2019• 29 citations
arXivHTMLPDF

Abstract

We present momentum-resolved spectral functions and band gaps from bare and self-consistent second-order perturbation theory for insulating periodic solids. We establish that, for systems with large gap sizes, both bare and self-consistent perturbation theory yield reasonable gaps. However, smaller gap sizes require a self-consistent adjustment of the propagator. In contrast to results obtained within a quasiparticle formalism used on top of bare second-order perturbation theory, no unphysical behavior of the band gap is observed. Our implementation of a fully self-consistent, $\mathrm{\ensuremath{\Phi}}$-derivable, and thermodynamically consistent finite-temperature diagrammatic perturbation theory forms a framework on which embedding theories such as the dynamical mean-field theory and self-energy embedding theories can be implemented.

DOI
10.1103/physrevb.100.085112

Related papers

Effect of propagator renormalization on the band gap of solids.

Sergei Iskakov, Alexander A. Rusakov, Dominika Zgid +1 more

We present momentum-resolved spectral functions and band gaps from bare and self-consistent second order perturbation theory for insulating periodic solids. We establish that, for systems with large gap sizes, both bare and self-consistent perturbation theory yield reasonable gaps. However, smaller gap sizes require a self-consistent adjustment of the propagator. In contrast to results obtained within a quasi-particle formalism used on top of bare second order perturbation theory, no unphysical behaviour of the band gap is observed. We establish that the renormalization or `screening' of interaction terms in addition to propagators is not required to obtain accurate gaps in insulators. Our implementation of a fully self-consistent, $\Phi$-derivable and thermodynamically consistent finite temperature diagrammatic perturbation theory forms a framework on which embedding theories such as the dynamical mean field theory or self-energy embedding theories can be implemented.

•Dec 17, 2018•0 citations

Self-consistent G W + extended dynamical mean field theory for semiconductors and insulators

Viktor Christiansson, Francesco Petocchi, Philipp Werner

Theoretical studies of semiconductors and band insulators are usually based on variants of the $GW$ method without full self-consistency, like single-shot $G^0W^0$ or quasiparticle self-consistent $GW$. Fully self-consistent $GW$ provides a poor description of the gap size and electronic structure due to the lack of vertex corrections. While it is hard to predict at which order corrections can be neglected, local vertex corrections to all orders can be consistently included by combining $GW$ with extended dynamical mean field theory (EDMFT). Here, we show that \textit{ab initio} multitier $GW$+EDMFT calculations, which achieve full self-consistency in a suitably defined low-energy space, provide an accurate description of semiconductors and band insulators, comparable to the established methods which are typically used for this class of materials. Our results demonstrate that the range of applicability of $GW$+EDMFT extends to weakly correlated systems, and they imply that despite the weak correlations, local vertex corrections are an important ingredient in the diagrammatic treatment of semiconductors and band insulators.

arXiv:2410.19579•Physical review. B./Physical review. B•Jun 12, 2026•0 citations

Correlations in a band insulator

Michael A. Sentef, J. Kuneš, Philipp Werner +1 more

We study a model of a covalent band insulator with on-site Coulomb repulsion at half filling using dynamical mean-field theory. Upon increasing the interaction strength the system undergoes a discontinuous transition from a correlated band insulator to a Mott insulator with hysteretic behavior at low temperatures. Increasing the temperature in the band insulator close to the insulator-insulator transition we find a crossover to a Mott insulator at elevated temperatures. Remarkably, correlations decrease the energy gap in the correlated band insulator. The gap renormalization can be traced to the low-frequency behavior of the self-energy, analogously to the quasiparticle renormalization in a Fermi liquid. While the uncorrelated band insulator is characterized by a single gap for both charge and spin excitations, the spin gap is smaller than the charge gap in the correlated system.

arXiv:0907.1237•Physical Review B•Oct 8, 2009•47 citations

Resolving finite-size errors in EOM-CCSD band gaps of solids with interacting-bath dynamical embedding theory

Jiachen Li, Christopher Hillenbrand, Christian Venturella +2 more

Periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD) has shown promise for quantitative calculations of band structures in solids. However, its steep computational scaling has limited calculations to relatively coarse k-point meshes, leading to sizable finite-size errors and discrepant estimates of thermodynamic-limit band gaps in recent benchmarks. In this work, we revisit EOM-CCSD band gaps for ten semiconductors and insulators using interacting-bath dynamical embedding theory (ibDET), a systematically improvable Green's function embedding framework that enables dense Brillouin-zone sampling at modest computational cost. By pushing the k-point sampling up to 10 × 10 × 10, well beyond the system sizes accessible in canonical periodic EOM-CCSD calculations, we significantly reduce finite-size errors and obtain stable thermodynamic-limit extrapolations. We further compare G0W0@PBE, G0W0@HF, and EOM-CCSD on an equal footing using the same numerical settings in PySCF. We find that EOM-CCSD yields a mean absolute error of 0.32 eV relative to experimental band gaps for a test set of ten semiconductors and insulators, which is lower than that of G0W0@PBE. For ZnO, EOM-CCSD also accurately describes the Zn 3d-band binding energy, despite overestimating the band gap. These results demonstrate that ibDET offers a practical route to high-accuracy many-body electronic structure calculations in periodic systems.

arXiv:2606.12621•The Journal of Chemical Physics•Sep 1, 2026•0 citations

Unified Approach to Polarons and Phonon-Induced Band Structure Renormalization

Jon Lafuente-Bartolome, Chao Lian, Weng Hong Sio +3 more

Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.

arXiv:2208.06346•Physical Review Letters•Aug 9, 2022•54 citations

Dynamical density-matrix renormalization group for the Mott–Hubbard insulator in high dimensions

Satoshi Nishimoto, Florian Gebhard, Eric Jeckelmann

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth $W=4t$ at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling $U_{\rm c}/t=4.45 \pm 0.05$. At $U=4.5t$, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at $U_{\rm c}$.

arXiv:cond-mat/0406666•Journal of Physics Condensed Matter•Sep 21, 2004•61 citations
We present momentum-resolved spectral functions and band gaps from bare and self-consistent second-order perturbation theory for insulating periodic solids. We establish that, for systems with large gap sizes, both bare and self-consistent perturbation theory yield reasonable gaps. However, smaller gap sizes require a self-consistent adjustment of the propagator. In contrast to results obtained within a quasiparticle formalism used on top of bare second-order perturbation theory, no unphysical behavior of the band gap is observed. Our implementation of a fully self-consistent, \ensuremathΦ\mathrm{\ensuremath{\Phi}}\ensuremathΦ-derivable, and thermodynamically consistent finite-temperature diagrammatic perturbation theory forms a framework on which embedding theories such as the dynamical mean-field theory and self-energy embedding theories can be implemented.
We present momentum-resolved spectral functions and band gaps from bare and self-consistent second order perturbation theory for insulating periodic solids. We establish that, for systems with large gap sizes, both bare and self-consistent perturbation theory yield reasonable gaps. However, smaller gap sizes require a self-consistent adjustment of the propagator. In contrast to results obtained within a quasi-particle formalism used on top of bare second order perturbation theory, no unphysical behaviour of the band gap is observed. We establish that the renormalization or `screening' of interaction terms in addition to propagators is not required to obtain accurate gaps in insulators. Our implementation of a fully self-consistent, Φ\PhiΦ-derivable and thermodynamically consistent finite temperature diagrammatic perturbation theory forms a framework on which embedding theories such as the dynamical mean field theory or self-energy embedding theories can be implemented.
Theoretical studies of semiconductors and band insulators are usually based on variants of the GWGWGW method without full self-consistency, like single-shot G0W0G^0W^0G0W0 or quasiparticle self-consistent GWGWGW. Fully self-consistent GWGWGW provides a poor description of the gap size and electronic structure due to the lack of vertex corrections. While it is hard to predict at which order corrections can be neglected, local vertex corrections to all orders can be consistently included by combining GWGWGW with extended dynamical mean field theory (EDMFT). Here, we show that \textit{ab initio} multitier GWGWGW+EDMFT calculations, which achieve full self-consistency in a suitably defined low-energy space, provide an accurate description of semiconductors and band insulators, comparable to the established methods which are typically used for this class of materials. Our results demonstrate that the range of applicability of GWGWGW+EDMFT extends to weakly correlated systems, and they imply that despite the weak correlations, local vertex corrections are an important ingredient in the diagrammatic treatment of semiconductors and band insulators.
We study a model of a covalent band insulator with on-site Coulomb repulsion at half filling using dynamical mean-field theory. Upon increasing the interaction strength the system undergoes a discontinuous transition from a correlated band insulator to a Mott insulator with hysteretic behavior at low temperatures. Increasing the temperature in the band insulator close to the insulator-insulator transition we find a crossover to a Mott insulator at elevated temperatures. Remarkably, correlations decrease the energy gap in the correlated band insulator. The gap renormalization can be traced to the low-frequency behavior of the self-energy, analogously to the quasiparticle renormalization in a Fermi liquid. While the uncorrelated band insulator is characterized by a single gap for both charge and spin excitations, the spin gap is smaller than the charge gap in the correlated system.
Periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD) has shown promise for quantitative calculations of band structures in solids. However, its steep computational scaling has limited calculations to relatively coarse k-point meshes, leading to sizable finite-size errors and discrepant estimates of thermodynamic-limit band gaps in recent benchmarks. In this work, we revisit EOM-CCSD band gaps for ten semiconductors and insulators using interacting-bath dynamical embedding theory (ibDET), a systematically improvable Green's function embedding framework that enables dense Brillouin-zone sampling at modest computational cost. By pushing the k-point sampling up to 10 × 10 × 10, well beyond the system sizes accessible in canonical periodic EOM-CCSD calculations, we significantly reduce finite-size errors and obtain stable thermodynamic-limit extrapolations. We further compare G0W0@PBE, G0W0@HF, and EOM-CCSD on an equal footing using the same numerical settings in PySCF. We find that EOM-CCSD yields a mean absolute error of 0.32 eV relative to experimental band gaps for a test set of ten semiconductors and insulators, which is lower than that of G0W0@PBE. For ZnO, EOM-CCSD also accurately describes the Zn 3d-band binding energy, despite overestimating the band gap. These results demonstrate that ibDET offers a practical route to high-accuracy many-body electronic structure calculations in periodic systems.
Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.
We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth W=4tW=4tW=4t at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling Uc/t=4.45±0.05U_{\rm c}/t=4.45 \pm 0.05Uc​/t=4.45±0.05. At U=4.5tU=4.5tU=4.5t, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at UcU_{\rm c}Uc​.