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:2501.05346 · Physical review. B./Physical review. B

Two-particle self-consistent approach combined with dynamical mean field theory: A real-frequency study of the square-lattice Hubbard model

Lei Geng, Jiawei Yan, Philipp Werner

Published Mar 20, 2025• 5 citations
arXivHTMLPDF

Abstract

We investigate the two-dimensional Hubbard model using a real-frequency implementation of the $\mathrm{TPSC}+\mathrm{DMFT}$ approach. This hybrid method combines the nonlocal correlations captured by the two-particle self-consistent (TPSC) approach with the local dynamical correlations of dynamical mean field theory (DMFT). The results demonstrate that $\mathrm{TPSC}+\mathrm{DMFT}$ effectively describes pseudogap physics and nonlocal fluctuations in the moderately correlated regime, while also reproducing the Mott insulating state at larger interaction strengths. For doped Mott insulators, we find that $\mathrm{TPSC}+\mathrm{DMFT}$ captures the evolution of Fermi pockets into Fermi arcs, consistent with the results from cluster DMFT and photoemission studies. These findings highlight the capability of $\mathrm{TPSC}+\mathrm{DMFT}$ to bridge the gap between weak and strong coupling physics in Hubbard models, providing insights into spin and charge fluctuations, as well as their role in the pseudogap formation.

DOI
10.1103/physrevb.111.115143

Related papers

Dynamical mean field theory extension to the nonequilibrium two-particle self-consistent approach

Olivier Simard, Philipp Werner

Nonlocal correlations play an essential role in correlated electron systems, especially in the vicinity of phase transitions and crossovers, where two-particle correlation functions display a distinct momentum dependence. In nonequilibrium settings, the effect of nonlocal correlations on dynamical phase transitions, prethermalization phenomena, and trapping in metastable states is not well understood. In this paper, we introduce a dynamical mean field theory (DMFT) extension to the nonequilibrium two-particle self-consistent (TPSC) approach, which allows to perform nonequilibrium simulations capturing short- and long-ranged nonlocal correlations in the weak-, intermediate-, and strong-correlation regimes. The method self-consistently computes local spin and charge vertices, from which a momentum-dependent self-energy is constructed. Replacing the local part of the self-energy by the DMFT result within this self-consistent scheme provides an improved description of local correlation effects. We explain the details of the formalism and the implementation, and demonstrate the versatility of DMFT+TPSC with interaction quenches and dimensional crossovers in the Hubbard model.

arXiv:2302.14134•Physical review. B./Physical review. B•Jun 27, 2023•9 citations

Nonlocal corrections to dynamical mean-field theory from the two-particle self-consistent method

N. Martin, C. Gauvin-Ndiaye, A.–M. S. Tremblay

Theoretical methods that are accurate for both short-distance observables and long-wavelength collective modes are still being developed for the Hubbard model. Here, we benchmark an approach that combines dynamical mean-field theory (DMFT) observables with the two-particle self-consistent theory (TPSC). This offers a way to include non-local correlations in DMFT while also improving TPSC. The benchmarks are published diagrammatic quantum Monte Carlo results for the two-dimensional square lattice Hubbard model with nearest-neighbor hopping. This method ($\mathrm{TPSC}+\mathrm{DMFT}$) is relevant for weak to intermediate interaction, satisfies the local Pauli principle, and allows us to compute a spin susceptibility that satisfies the Mermin-Wagner theorem. The DMFT double occupancy determines the spin and charge vertices through local spin and charge sum rules. The TPSC self-energy is also improved by replacing its local part with the local DMFT self-energy. With this method, we find improvements for both spin and charge fluctuations and for the self-energy. We also find that the accuracy check developed for TPSC is a good predictor of deviations from benchmarks for this model. $\mathrm{TPSC}+\mathrm{DMFT}$ can be used in regimes where quantum Monte Carlo is inaccessible. In addition, this method paves the way to multiband generalizations of TPSC that could be used in advanced electronic structure codes that include DMFT.

arXiv:2211.01919•Physical review. B./Physical review. B•Feb 28, 2023•14 citations

Pseudogaps in strongly correlated metals: A generalized dynamical mean-field theory approach

Michael V. Sadovskii, I. A. Nekrasov, É. Z. Kuchinskiǐ +2 more

We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale $\ensuremath{\xi}$ via a momentum dependent external self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$. This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave--like antiferromagnetic spin (or the charge density wave--like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth $W\ensuremath{\lesssim}U$ ($U$---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.

arXiv:cond-mat/0508585•Physical Review B•Oct 6, 2005•140 citations

Pseudogaps: introducing the length scale into dynamical mean-field theory

É. Z. Kuchinskiǐ, I. A. Nekrasov, Michael V. Sadovskii

Pseudogap physics in strongly correlated systems is essentially scale dependent. We generalize the dynamical mean-field theory (DMFT) by introducing into the DMFT equations dependence on the correlation length of pseudogap fluctuations via an additional (momentum-dependent) self-energy Σk. This self-energy describes nonlocal dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT +Σk approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest- and next-nearest-neighbor hopping. The effective single impurity problem is solved by the numerical renormalization group (NRG). Both types of strongly correlated metals, namely (i) the doped Mott insulator and (ii) the case of bandwidth W≲U (U is the value of local Coulomb interaction) are considered. Densities of states, spectral functions and ARPES spectra calculated within DMFT +Σk show a pseudogap formation near the Fermi level of the quasiparticle band. We also briefly discuss effects of random impurity scattering. Finally we demonstrate a qualitative picture of Fermi surface “destruction” due to pseudogap fluctuations and formation of “Fermi arcs” which agrees well with ARPES observations.

Low Temperature Physics•Apr 1, 2006•23 citations

Generalized dynamical mean-field theory in the physics of strongly correlated systems

Eduard Z Kuchinskii, I. A. Nekrasov, Mikhail V Sadovskii

This review is devoted to generalization of dynamical mean-field theory (DMFT) for strongly correlated electronic systems towards the account of different types of additional interactions, necessary for correct physical description of many experimentally observed phenomena in such systems. As additional interactions we consider: (1) interaction of electrons with antiferromagnetic (or charge) fluctuations of order parameter in high-Tc superconductors leading to the formation of pseudogap state, (2) scattering of electrons on static disorder and its role in general picture of Anderson-Hubbard metal-insulator transition, (3) electron-phonon interaction and corresponding anomalies of electronic spectra in strongly correlated systems. Proposed DMFT+Sigma approach is based on taking into account above mentioned interactions by introducing additional self-energy Sigma (in general momentum dependent) into conventional DMFT scheme and calculated in a self-consistent way within the standard set of DMFT equations. Here we formulate general scheme of calculation of both one-particle (spectral functions and densities of states) and two-particle (optical conductivity) properties. We examine the problem of pseudogap formation, including the Fermi arc formation and partial destruction of the Fermi surface, metal-insulator transition in disordered Anderson-Hubbard model, and general picture of kink formation within electronic spectra in strongly correlated systems. DMFT+Sigma approach is generalized to describe realistic materials with strong electron-electron correlations based on LDA+DMFT method. General scheme of LDA+DMFT method is presented together with some of its applications to real systems. The LDA+DMFT+Sigma approach is employed to modelling of pseudogap state of electron and hole doped high-T_c cuprates. Comparison with variety of ARPES experiments is given.

arXiv:1109.2305•Physics-Uspekhi•Apr 30, 2012•63 citations

Mott physics and spin fluctuations: A unified framework

Thomas Ayral, Olivier Parcollet

We present a formalism for strongly correlated electron systems which consists in a local approximation of the dynamical three-leg interaction vertex. This vertex is self-consistently computed using a quantum impurity model with dynamical interactions in the charge and spin channels, similar to dynamical mean field theory approaches. The electronic self-energy and the polarization are both frequency and momentum dependent. The method interpolates between the spin-fluctuation or GW approximations at weak coupling and the atomic limit at strong coupling. We apply the formalism to the Hubbard model on a two-dimensional square lattice and show that as interactions are increased towards the Mott insulating state, the local vertex acquires a strong frequency dependence, driving the system to a Mott transition, while at low enough temperatures the momentum dependence of the self-energy is enhanced due to large spin fluctuations. Upon doping, we find a Fermi arc in the one-particle spectral function, which is one signature of the pseudogap state.

arXiv:1503.07724•Physical Review B•Sep 3, 2015•153 citations
We investigate the two-dimensional Hubbard model using a real-frequency implementation of the TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT approach. This hybrid method combines the nonlocal correlations captured by the two-particle self-consistent (TPSC) approach with the local dynamical correlations of dynamical mean field theory (DMFT). The results demonstrate that TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT effectively describes pseudogap physics and nonlocal fluctuations in the moderately correlated regime, while also reproducing the Mott insulating state at larger interaction strengths. For doped Mott insulators, we find that TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT captures the evolution of Fermi pockets into Fermi arcs, consistent with the results from cluster DMFT and photoemission studies. These findings highlight the capability of TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT to bridge the gap between weak and strong coupling physics in Hubbard models, providing insights into spin and charge fluctuations, as well as their role in the pseudogap formation.
Nonlocal correlations play an essential role in correlated electron systems, especially in the vicinity of phase transitions and crossovers, where two-particle correlation functions display a distinct momentum dependence. In nonequilibrium settings, the effect of nonlocal correlations on dynamical phase transitions, prethermalization phenomena, and trapping in metastable states is not well understood. In this paper, we introduce a dynamical mean field theory (DMFT) extension to the nonequilibrium two-particle self-consistent (TPSC) approach, which allows to perform nonequilibrium simulations capturing short- and long-ranged nonlocal correlations in the weak-, intermediate-, and strong-correlation regimes. The method self-consistently computes local spin and charge vertices, from which a momentum-dependent self-energy is constructed. Replacing the local part of the self-energy by the DMFT result within this self-consistent scheme provides an improved description of local correlation effects. We explain the details of the formalism and the implementation, and demonstrate the versatility of DMFT+TPSC with interaction quenches and dimensional crossovers in the Hubbard model.
Theoretical methods that are accurate for both short-distance observables and long-wavelength collective modes are still being developed for the Hubbard model. Here, we benchmark an approach that combines dynamical mean-field theory (DMFT) observables with the two-particle self-consistent theory (TPSC). This offers a way to include non-local correlations in DMFT while also improving TPSC. The benchmarks are published diagrammatic quantum Monte Carlo results for the two-dimensional square lattice Hubbard model with nearest-neighbor hopping. This method (TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT) is relevant for weak to intermediate interaction, satisfies the local Pauli principle, and allows us to compute a spin susceptibility that satisfies the Mermin-Wagner theorem. The DMFT double occupancy determines the spin and charge vertices through local spin and charge sum rules. The TPSC self-energy is also improved by replacing its local part with the local DMFT self-energy. With this method, we find improvements for both spin and charge fluctuations and for the self-energy. We also find that the accuracy check developed for TPSC is a good predictor of deviations from benchmarks for this model. TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT can be used in regimes where quantum Monte Carlo is inaccessible. In addition, this method paves the way to multiband generalizations of TPSC that could be used in advanced electronic structure codes that include DMFT.
We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale $\ensuremath{\xi}$ via a momentum dependent external self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$. This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave--like antiferromagnetic spin (or the charge density wave--like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth $W\ensuremath{\lesssim}U$ (UUU---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.
Pseudogap physics in strongly correlated systems is essentially scale dependent. We generalize the dynamical mean-field theory (DMFT) by introducing into the DMFT equations dependence on the correlation length of pseudogap fluctuations via an additional (momentum-dependent) self-energy Σk. This self-energy describes nonlocal dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT +Σk approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest- and next-nearest-neighbor hopping. The effective single impurity problem is solved by the numerical renormalization group (NRG). Both types of strongly correlated metals, namely (i) the doped Mott insulator and (ii) the case of bandwidth W≲U (U is the value of local Coulomb interaction) are considered. Densities of states, spectral functions and ARPES spectra calculated within DMFT +Σk show a pseudogap formation near the Fermi level of the quasiparticle band. We also briefly discuss effects of random impurity scattering. Finally we demonstrate a qualitative picture of Fermi surface “destruction” due to pseudogap fluctuations and formation of “Fermi arcs” which agrees well with ARPES observations.
This review is devoted to generalization of dynamical mean-field theory (DMFT) for strongly correlated electronic systems towards the account of different types of additional interactions, necessary for correct physical description of many experimentally observed phenomena in such systems. As additional interactions we consider: (1) interaction of electrons with antiferromagnetic (or charge) fluctuations of order parameter in high-Tc superconductors leading to the formation of pseudogap state, (2) scattering of electrons on static disorder and its role in general picture of Anderson-Hubbard metal-insulator transition, (3) electron-phonon interaction and corresponding anomalies of electronic spectra in strongly correlated systems. Proposed DMFT+Sigma approach is based on taking into account above mentioned interactions by introducing additional self-energy Sigma (in general momentum dependent) into conventional DMFT scheme and calculated in a self-consistent way within the standard set of DMFT equations. Here we formulate general scheme of calculation of both one-particle (spectral functions and densities of states) and two-particle (optical conductivity) properties. We examine the problem of pseudogap formation, including the Fermi arc formation and partial destruction of the Fermi surface, metal-insulator transition in disordered Anderson-Hubbard model, and general picture of kink formation within electronic spectra in strongly correlated systems. DMFT+Sigma approach is generalized to describe realistic materials with strong electron-electron correlations based on LDA+DMFT method. General scheme of LDA+DMFT method is presented together with some of its applications to real systems. The LDA+DMFT+Sigma approach is employed to modelling of pseudogap state of electron and hole doped high-T_c cuprates. Comparison with variety of ARPES experiments is given.
We present a formalism for strongly correlated electron systems which consists in a local approximation of the dynamical three-leg interaction vertex. This vertex is self-consistently computed using a quantum impurity model with dynamical interactions in the charge and spin channels, similar to dynamical mean field theory approaches. The electronic self-energy and the polarization are both frequency and momentum dependent. The method interpolates between the spin-fluctuation or GW approximations at weak coupling and the atomic limit at strong coupling. We apply the formalism to the Hubbard model on a two-dimensional square lattice and show that as interactions are increased towards the Mott insulating state, the local vertex acquires a strong frequency dependence, driving the system to a Mott transition, while at low enough temperatures the momentum dependence of the self-energy is enhanced due to large spin fluctuations. Upon doping, we find a Fermi arc in the one-particle spectral function, which is one signature of the pseudogap state.