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:2101.04466 · Physical review. B./Physical review. B

Development of an efficient impurity solver in dynamical mean field theory for multiband systems: Iterative perturbation theory combined with parquet equations

Ryota Mizuno, Masayuki Ochi, Kazuhiko Kuroki

Published Jul 30, 2021• 6 citations
arXivHTMLPDF

Abstract

Although several impurity solvers in the dynamical mean field theory (DMFT) have been proposed, especially in multiband systems, there are practical difficulties arising from a trade-off between numerical costs and reliability. In this study, we reinterpret the iterative perturbation theory (IPT) as an approximation which captures the strong correlation effects by mimicking the particular frequency structures of the exact full vertex, and extend it such that it can have efficiency and reliability simultaneously by modifying IPT vertex using the parquet equations. We apply this method to several models to evaluate their validity. We confirm that our method shows good agreements with the numerically exact continuous-time quantum Monte Carlo method in the single-site DMFT calculation.

DOI
10.1103/physrevb.104.035160

Related papers

Study on the validity of IPT+parquet method as an impurity solver in DMFT focusing on orbital fluctuations

Aira Yamada, Ryota Mizuno, Masayuki Ochi +2 more

A breakdown of calculations with exact impurity solvers in the dynamical mean field theory in multiband systems easily occurs due to the expensive numerical cost. To overcome this practical difficulty, three of the present authors developed an inexpensive and reliable impurity solver by combining the iterative perturbation theory (IPT) and parquet equation, and named it IPT+parquet [R. Mizuno, et al., Phys. Rev. B 104, 035160 (2021).]. In this study, we validate IPT+parquet focusing on the orbital fluctuation by comparing the numerically exact impurity solvers. We confirm that IPT+parquet can capture competition between orbital fluctuation channels, which the conventional IPT cannot capture.

arXiv:2606.05822•Jun 4, 2026•0 citations

Development of efficient approximation methods in dynamical mean field theory for multi-degree-of-freedom systems

Ryota Mizuno, Masayuki Ochi, Kazuhiko Kuroki

Although several impurity solvers in the dynamical mean field theory (DMFT) have been proposed, especially in multi-degree-of-freedom systems, there are practical difficulties arising from a trade-off between numerical costs and reliability. In this study, we re-interpret the iterative perturbation theory (IPT) from the perspective of the frequency dependence, and extend it such that costs and reliability can be compatible. From the same perspective, we also develop the methods in which the dual fermion calculation can be performed efficiently and can be combined with any impurity solver. We apply these methods to several models to evaluate their validity. We confirm that our methods show good agreements with the numerically exact continuous-time quantum Monte Carlo (CT-QMC) method in the local DMFT calculation, and can also capture important behaviors such as the pseudo gap in the DMFT + non-local calculation. In addition, the numerical costs are kept sufficiently small.

•Jan 12, 2021•0 citations

An Efficient and Well-Benchmarked Multi-Orbital Impurity Solver for Predictive Investigations of Correlated Materials

Gurshidali P., N. S. Vidhyadhiraja

Predicting the physical properties of strongly correlated electron systems (SCES) requires the combined Density Functional Theory and Dynamical Mean-Field Theory (DFT+DMFT) framework. However, the computational bottle-neck lies in the impurity solver. This work focuses on rigorously benchmarking the Multi-Orbital Iterated Perturbation Theory (MO-IPT) impurity solver against the numerically exact Continuous-Time Quantum Monte Carlo (CTQMC) method, specifically through a detailed study of the three-orbital Hubbard model. The two-orbital model serves as a canonical system to test performance under realistic multi-band conditions. Our systematically derived MO-IPT overcomes the critical limitations of CTQMC, including exponential scaling with orbital number, the need for analytic continuation, and the severe fermionic sign problem. By demonstrating high accuracy across varying interaction strengths and temperatures, we validate MO-IPT as an inexpensive, yet reliable, replacement solver essential for future material-specific investigations.

IEEE International Conference on High Performance Computing, Data and Analytics Workshop (HiPCW)•Dec 17, 2025•0 citations

A Mathematical Analysis of IPT-DMFT

Eric Cancès B, Alfred Kirsch, Solal Perrin-Roussel

Abstract We provide a mathematical analysis of the Dynamical Mean-Field Theory (DMFT), a celebrated representative of a class of approximations in quantum mechanics known as embedding methods . Within the simplest setting of this approximation, which we introduce briefly at this point, we prove that, under certain assumptions, the DMFT equations admit a solution for any set of physical parameters. Moreover, we establish some properties of the solution(s). For the reader’s convenience, we provide in appendix a pedagogical and self-contained mathematical formulation of the DMFT equations for the finite Hubbard model. After recalling the definition and properties of one-body time-ordered Green’s functions and self-energies, and the mathematical structure of the Hubbard and Anderson impurity models, we describe the specific impurity solver we have studied in this article, namely the Iterated Perturbation Theory (IPT) solver, which can be conveniently formulated using Matsubara’s Green’s functions.

arXiv:2406.03384•Communications in Mathematical Physics•Jun 6, 2026•0 citations

Benchmark of a modified iterated perturbation theory approach on the fcc lattice at strong coupling

Louis-François Arsenault, P. Sémon, A.–M. S. Tremblay

The dynamical mean-field theory approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of noninteracting electrons. Iterated perturbation theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact continuous-time quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-$D$. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy, and specific heat on the fcc lattice are calculated with both IPT-$D$ and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-$D$. Particle-hole asymmetry persists even at coupling twice the bandwidth. A generalization to the multiorbital case is suggested. Several algorithms that speed up the calculations are described in appendixes.

arXiv:1202.5814•Physical Review B•Aug 22, 2012•44 citations

Strong-coupling solver for the quantum impurity model

Xi Dai, Kristjan Haule, Gabriel Kotliar

We propose a fast impurity solver for the general quantum impurity model based on the perturbation theory around the atomic limit, which can be used in combination with the local density approximation (LDA) and the dynamical mean-field theory (DMFT). We benchmark the solver in the two-band Hubbard model within DMFT against quantum Monte Carlo (QMC) and numerical renormalization-group (NRG) results. We find that the solver works very well in the paramagnetic Mott insulator phase. We also apply this impurity solver to the DMFT study of the antiferromagnetic phase transition in the unfrustrated Bethe lattice. The Neel temperature obtained by the fast impurity solver agrees very well with the QMC results in the large Hubbard U limit. The method is a promising tool to be used in combination with the $\mathrm{LDA}+\mathrm{DMFT}$ to study Mott insulators starting from first principles.

arXiv:cond-mat/0412505•Physical Review B•Jul 8, 2005•26 citations
Although several impurity solvers in the dynamical mean field theory (DMFT) have been proposed, especially in multiband systems, there are practical difficulties arising from a trade-off between numerical costs and reliability. In this study, we reinterpret the iterative perturbation theory (IPT) as an approximation which captures the strong correlation effects by mimicking the particular frequency structures of the exact full vertex, and extend it such that it can have efficiency and reliability simultaneously by modifying IPT vertex using the parquet equations. We apply this method to several models to evaluate their validity. We confirm that our method shows good agreements with the numerically exact continuous-time quantum Monte Carlo method in the single-site DMFT calculation.
A breakdown of calculations with exact impurity solvers in the dynamical mean field theory in multiband systems easily occurs due to the expensive numerical cost. To overcome this practical difficulty, three of the present authors developed an inexpensive and reliable impurity solver by combining the iterative perturbation theory (IPT) and parquet equation, and named it IPT+parquet [R. Mizuno, et al., Phys. Rev. B 104, 035160 (2021).]. In this study, we validate IPT+parquet focusing on the orbital fluctuation by comparing the numerically exact impurity solvers. We confirm that IPT+parquet can capture competition between orbital fluctuation channels, which the conventional IPT cannot capture.
Although several impurity solvers in the dynamical mean field theory (DMFT) have been proposed, especially in multi-degree-of-freedom systems, there are practical difficulties arising from a trade-off between numerical costs and reliability. In this study, we re-interpret the iterative perturbation theory (IPT) from the perspective of the frequency dependence, and extend it such that costs and reliability can be compatible. From the same perspective, we also develop the methods in which the dual fermion calculation can be performed efficiently and can be combined with any impurity solver. We apply these methods to several models to evaluate their validity. We confirm that our methods show good agreements with the numerically exact continuous-time quantum Monte Carlo (CT-QMC) method in the local DMFT calculation, and can also capture important behaviors such as the pseudo gap in the DMFT + non-local calculation. In addition, the numerical costs are kept sufficiently small.
Predicting the physical properties of strongly correlated electron systems (SCES) requires the combined Density Functional Theory and Dynamical Mean-Field Theory (DFT+DMFT) framework. However, the computational bottle-neck lies in the impurity solver. This work focuses on rigorously benchmarking the Multi-Orbital Iterated Perturbation Theory (MO-IPT) impurity solver against the numerically exact Continuous-Time Quantum Monte Carlo (CTQMC) method, specifically through a detailed study of the three-orbital Hubbard model. The two-orbital model serves as a canonical system to test performance under realistic multi-band conditions. Our systematically derived MO-IPT overcomes the critical limitations of CTQMC, including exponential scaling with orbital number, the need for analytic continuation, and the severe fermionic sign problem. By demonstrating high accuracy across varying interaction strengths and temperatures, we validate MO-IPT as an inexpensive, yet reliable, replacement solver essential for future material-specific investigations.
Abstract We provide a mathematical analysis of the Dynamical Mean-Field Theory (DMFT), a celebrated representative of a class of approximations in quantum mechanics known as embedding methods . Within the simplest setting of this approximation, which we introduce briefly at this point, we prove that, under certain assumptions, the DMFT equations admit a solution for any set of physical parameters. Moreover, we establish some properties of the solution(s). For the reader’s convenience, we provide in appendix a pedagogical and self-contained mathematical formulation of the DMFT equations for the finite Hubbard model. After recalling the definition and properties of one-body time-ordered Green’s functions and self-energies, and the mathematical structure of the Hubbard and Anderson impurity models, we describe the specific impurity solver we have studied in this article, namely the Iterated Perturbation Theory (IPT) solver, which can be conveniently formulated using Matsubara’s Green’s functions.
The dynamical mean-field theory approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of noninteracting electrons. Iterated perturbation theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact continuous-time quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-DDD. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy, and specific heat on the fcc lattice are calculated with both IPT-DDD and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-DDD. Particle-hole asymmetry persists even at coupling twice the bandwidth. A generalization to the multiorbital case is suggested. Several algorithms that speed up the calculations are described in appendixes.
We propose a fast impurity solver for the general quantum impurity model based on the perturbation theory around the atomic limit, which can be used in combination with the local density approximation (LDA) and the dynamical mean-field theory (DMFT). We benchmark the solver in the two-band Hubbard model within DMFT against quantum Monte Carlo (QMC) and numerical renormalization-group (NRG) results. We find that the solver works very well in the paramagnetic Mott insulator phase. We also apply this impurity solver to the DMFT study of the antiferromagnetic phase transition in the unfrustrated Bethe lattice. The Neel temperature obtained by the fast impurity solver agrees very well with the QMC results in the large Hubbard U limit. The method is a promising tool to be used in combination with the LDA+DMFT\mathrm{LDA}+\mathrm{DMFT}LDA+DMFT to study Mott insulators starting from first principles.