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

IEEE International Conference on High Performance Computing, Data and Analytics Workshop (HiPCW)

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

Gurshidali P., N. S. Vidhyadhiraja

Published Dec 17, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1109/hipcw66559.2025.00031

Related papers

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

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.

arXiv:2101.04466•Physical review. B./Physical review. B•Jul 30, 2021•6 citations

Continuous Time Quantum Monte Carlo in Combination with Machine Learning on the Hubbard Model

Hunpyo Lee

The acceleration of exact continuous time quantum Monte Carlo (CTQMC) approaches in multi-site or multi-orbital systems is extremely interesting work, because these approaches are very time-consuming in terms of numerical computation and might account for the nature of exotic behaviors such as high-temperature superconductivity and Mott insulator behavior observed in the strongly correlated materials. We extend the recently developed interaction-expansion CTQMC method in combination with a machine learning (CTQMC+ML) approach for the single-site and single-orbital systems to multi-site and multi-orbital ones. This method can be applied to explore the nonlocal correlation effects in lattice models and to study the electronic structure of real materials via an ab-initio density functional theory plus dynamical mean field theory approach. We find that our CTQMC+ML method for multi-site (and multi-orbital) systems accurately predicts the impurity Green’s function with less computational time than the CTQMC approaches, as in the case of the single-site and single-orbital version.

Journal of the Korean Physical Society•Nov 1, 2019•1 citation

Hubb_DMFT and Wan2mb_DMFT: Continuous-Time Quantum Monte Carlo Solvers for Single- and Multi-Orbital Hubbard Model

A. A. Katanin

We present two related customized software packages, Hubb_DMFT and Wan2mb_DMFT, designed to solve the Dynamical Mean-Field Theory (DMFT) equations for strongly correlated electron systems. Hubb_DMFT is adjusted for the single-band Hubbard model, providing a fast way to calculate the local self-energy, as well as the two-particle fermion and triangular fermion-boson charge and spin vertices, while Wan2mb_DMFT extends this capability to realistic multi-orbital systems, directly interfacing Wannier tight-binding Hamiltonians with many-body solvers. Both codes are based on iQIST v.0.7 impurity solver and utilize a modified and internally integrated Continuous-Time Quantum Monte Carlo (CT-QMC) core with the hybridization expansion (CT-HYB) framework and improved self-energy and vertex estimators for density-density interaction, ensuring numerically exact solutions for quantum impurity problems.

arXiv:2608.18540•Aug 19, 2026•0 citations

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

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
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.
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.
The acceleration of exact continuous time quantum Monte Carlo (CTQMC) approaches in multi-site or multi-orbital systems is extremely interesting work, because these approaches are very time-consuming in terms of numerical computation and might account for the nature of exotic behaviors such as high-temperature superconductivity and Mott insulator behavior observed in the strongly correlated materials. We extend the recently developed interaction-expansion CTQMC method in combination with a machine learning (CTQMC+ML) approach for the single-site and single-orbital systems to multi-site and multi-orbital ones. This method can be applied to explore the nonlocal correlation effects in lattice models and to study the electronic structure of real materials via an ab-initio density functional theory plus dynamical mean field theory approach. We find that our CTQMC+ML method for multi-site (and multi-orbital) systems accurately predicts the impurity Green’s function with less computational time than the CTQMC approaches, as in the case of the single-site and single-orbital version.
We present two related customized software packages, Hubb_DMFT and Wan2mb_DMFT, designed to solve the Dynamical Mean-Field Theory (DMFT) equations for strongly correlated electron systems. Hubb_DMFT is adjusted for the single-band Hubbard model, providing a fast way to calculate the local self-energy, as well as the two-particle fermion and triangular fermion-boson charge and spin vertices, while Wan2mb_DMFT extends this capability to realistic multi-orbital systems, directly interfacing Wannier tight-binding Hamiltonians with many-body solvers. Both codes are based on iQIST v.0.7 impurity solver and utilize a modified and internally integrated Continuous-Time Quantum Monte Carlo (CT-QMC) core with the hybridization expansion (CT-HYB) framework and improved self-energy and vertex estimators for density-density interaction, ensuring numerically exact solutions for quantum impurity problems.
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.
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.