journal article·2025-03-31Open access

Ab initio dynamical mean field theory with natural orbitals renormalization group impurity solver

Jia-Ming Wang, Jing-Xuan Wang, Rong-Qiang He, Li Huang, Zhong-Yi Lu

npj Computational Materials· Volume 11· Issue 1

Abstract

Abstract In this study, we introduce a novel implementation of density functional theory integrated with single-site dynamical mean-field theory to investigate the complex properties of strongly correlated materials. This ab initio many-body computational toolkit, termed , utilizes the and codes to perform first-principles calculations and generate band structures for realistic materials. The challenges associated with correlated electron systems are addressed through two distinct yet complementary quantum impurity solvers: the natural orbitals renormalization group solver for zero temperature and the hybridization expansion continuous-time quantum Monte Carlo solver for finite temperatures. To validate the performance of this toolkit, we examine three representative cases: correlated metal SrVO3, unconventional superconductor La3Ni2O7, and Mott insulator MnO. The calculated results exhibit excellent agreement with previously available experimental and theoretical findings. Thus, it is suggested that the toolkit is proficient in accurately describing the electronic structures of d-electron correlated materials.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Physics of Superconductivity and Magnetism · Magnetic and transport properties of perovskites and related materials · Advanced Condensed Matter Physics

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (100+)

Show source-provided references
1. Morosan, E., Natelson, D., Nevidomskyy, A. H. & Si, Q. Strongly correlated materials. Adv. Mater. 24, 4896–4923 (2012).10.1002/adma.201202018 ↗
2. Imada, M., Fujimori, A. & Tokura, Y. Metal-insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998).10.1103/RevModPhys.70.1039 ↗
3. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).10.1103/RevModPhys.78.17 ↗
4. Dai, P. Antiferromagnetic order and spin dynamics in iron-based superconductors. Rev. Mod. Phys. 87, 855–896 (2015).10.1103/RevModPhys.87.855 ↗
5. Weng, Z. F., Smidman, M., Jiao, L., Lu, X. & Yuan, H. Q. Multiple quantum phase transitions and superconductivity in Ce-based heavy fermions. Rep. Prog. Phys. 79, 094503 (2016).10.1088/0034-4885/79/9/094503 ↗
6. Bauer, E. & Thompson, J. Plutonium-based heavy-Fermion systems. Annu. Rev. Condens. Matter Phys. 6, 137–153 (2015).10.1146/annurev-conmatphys-031214-014508 ↗
7. Anisimov, V. I., Zaanen, J. & Andersen, O. K. Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B 44, 943–954 (1991).10.1103/PhysRevB.44.943 ↗
8. Stewart, G. R. Non-Fermi-liquid behavior in d- and f-electron metals. Rev. Mod. Phys. 73, 797–855 (2001).10.1103/RevModPhys.73.797 ↗
9. Kent, P. R. C. & Kotliar, G. Toward a predictive theory of correlated materials. Science 361, 348–354 (2018).10.1126/science.aat5975 ↗
10. Vollhardt, D. Dynamical mean-field theory for correlated electrons. Ann. Phys. 524, 1–19 (2012).10.1002/andp.201100250 ↗
11. Georges, A., Kotliar, G., Krauth, W. & Rozenberg, M. J. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys. 68, 13–125 (1996).10.1103/RevModPhys.68.13 ↗
12. Song, Y., Wortis, R. & Atkinson, W. A. Dynamical mean field study of the two-dimensional disordered Hubbard model. Phys. Rev. B 77, 054202 (2008).10.1103/PhysRevB.77.054202 ↗
13. Miranda, E. & Dobrosavljević, V. Dynamical mean-field theories of correlation and disorder. In Conductor-Insulator Quantum Phase Transitions https://doi.org/10.1093/acprof:oso/9780199592593.003.0006 (Oxford University Press, 2012).10.1093/acprof:oso/9780199592593.003.0006 ↗
14. Aoki, H. et al. Nonequilibrium dynamical mean-field theory and its applications. Rev. Mod. Phys. 86, 779–837 (2014).10.1103/RevModPhys.86.779 ↗
15. Held, K. Electronic structure calculations using dynamical mean field theory. Adv. Phys. 56, 829–926 (2007).10.1080/00018730701619647 ↗
16. Kotliar, G. et al. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys. 78, 865–951 (2006).10.1103/RevModPhys.78.865 ↗
17. Anisimov, V. I., Poteryaev, A. I., Korotin, M. A., Anokhin, A. O. & Kotliar, G. First-principles calculations of the electronic structure and spectra of strongly correlated systems: dynamical mean-field theory. J. Phys. 9, 7359 (1997).
18. Shilenko, D. A. & Leonov, I. V. Correlated electronic structure, orbital-selective behavior, and magnetic correlations in double-layer La3Ni2O7 under pressure. Phys. Rev. B 108, 125105 (2023).10.1103/PhysRevB.108.125105 ↗
19. Wang, J.-X., Ouyang, Z., He, R.-Q. & Lu, Z.-Y. Non-Fermi liquid and Hund correlation in La4Ni3O10 under high pressure. Phys. Rev. B 109, 165140 (2024).10.1103/PhysRevB.109.165140 ↗
20. Aichhorn, M., Biermann, S., Miyake, T., Georges, A. & Imada, M. Theoretical evidence for strong correlations and incoherent metallic state in FeSe. Phys. Rev. B 82, 064504 (2010).10.1103/PhysRevB.82.064504 ↗
21. Craco, L. & Leoni, S. Theory of two-fluid metallicity in superconducting FeSe at high pressure. Phys. Rev. B 100, 121101 (2019).10.1103/PhysRevB.100.121101 ↗
22. Huang, L. & Lu, H. Signatures of Hundness in kagome metals. Phys. Rev. B 102, 125130 (2020).10.1103/PhysRevB.102.125130 ↗
23. Liu, Z. et al. Orbital-selective Dirac fermions and extremely flat bands in frustrated kagome-lattice metal CoSn. Nat. Commun. 11, 4002 (2020).10.1038/s41467-020-17462-4 ↗
24. Wan, S., Lu, H. & Huang, L. Temperature dependence of correlated electronic states in the archetypal kagome metal CoSn. Phys. Rev. B 105, 155131 (2022).10.1103/PhysRevB.105.155131 ↗
25. Huang, L. & Lu, H. Protracted Kondo screening and kagome bands in the heavy-fermion metal Ce3Al. Phys. Rev. B 102, 155140 (2020).10.1103/PhysRevB.102.155140 ↗
26. Shim, J. H., Haule, K. & Kotliar, G. Modeling the localized-to-itinerant electronic transition in the heavy Fermion system CeIrIn5. Science 318, 1615–1617 (2007).10.1126/science.1149064 ↗
27. Lu, H. & Huang, L. Pressure-driven 4f localized-itinerant crossover in heavy-fermion compound CeIn3: a first-principles many-body perspective. Phys. Rev. B 94, 075132 (2016).10.1103/PhysRevB.94.075132 ↗
28. Wallerberger, M. et al. w2dynamics: local one- and two-particle quantities from dynamical mean field theory. Comput. Phys. Commun. 235, 388–399 (2019).10.1016/j.cpc.2018.09.007 ↗
29. Aichhorn, M. et al. TRIQS/DFTTools: a TRIQS application for ab initio calculations of correlated materials. Comput. Phys. Commun. 204, 200–208 (2016).10.1016/j.cpc.2016.03.014 ↗
30. Parcollet, O. et al. TRIQS: a toolbox for research on interacting quantum systems. Comput. Phys. Commun. 196, 398–415 (2015).10.1016/j.cpc.2015.04.023 ↗
31. Seth, P., Krivenko, I., Ferrero, M. & Parcollet, O. TRIQS/CTHYB: a continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impurity problems. Comput. Phys. Commun. 200, 274–284 (2016).10.1016/j.cpc.2015.10.023 ↗
32. Gaenko, A. et al. Updated core libraries of the ALPS project. Comput. Phys. Commun. 213, 235–251 (2017).10.1016/j.cpc.2016.12.009 ↗
33. Shinaoka, H., Gull, E. & Werner, P. Continuous-time hybridization expansion quantum impurity solver for multi-orbital systems with complex hybridizations. Comput. Phys. Commun. 215, 128–136 (2017).10.1016/j.cpc.2017.01.003 ↗
34. Haule, K., Yee, C.-H. & Kim, K. Dynamical mean-field theory within the full-potential methods: Electronic structure of CeIrIn5, CeCoIn5, and CeRhIn5. Phys. Rev. B 81, 195107 (2010).10.1103/PhysRevB.81.195107 ↗
35. Haule, K. Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base. Phys. Rev. B 75, 155113 (2007).10.1103/PhysRevB.75.155113 ↗
36. Haule, K. Exact double counting in combining the dynamical mean field theory and the density functional theory. Phys. Rev. Lett. 115, 196403 (2015).10.1103/PhysRevLett.115.196403 ↗
37. Shinaoka, H., Otsuki, J., Kawamura, M., Takemori, N. & Yoshimi, K. DCore: integrated DMFT software for correlated electrons. SciPost Phys. 10, 117 (2021).10.21468/SciPostPhys.10.5.117 ↗
38. Pashov, D. et al. Questaal: a package of electronic structure methods based on the linear muffin-tin orbital technique. Comput. Phys. Commun. 249, 107065 (2020).10.1016/j.cpc.2019.107065 ↗
39. Amadon, B. et al. Plane-wave based electronic structure calculations for correlated materials using dynamical mean-field theory and projected local orbitals. Phys. Rev. B 77, 205112 (2008).10.1103/PhysRevB.77.205112 ↗
40. Amadon, B. A self-consistent DFT + DMFT scheme in the projector augmented wave method: applications to cerium, Ce2O3 and Pu2O3 with the Hubbard I solver and comparison to DFT + U. J. Phys.: Condens. Matter 24, 075604 (2012).
41. Gonze, X. et al. The Abinit project: Impact, environment and recent developments. Comput. Phys. Commun. 248, 107042 (2020).10.1016/j.cpc.2019.107042 ↗
42. Qu, X. et al. Density functional theory plus dynamical mean field theory within the framework of linear combination of numerical atomic orbitals: formulation and benchmarks. J. Chem. Theory Comput. 18, 5589–5606 (2022).10.1021/acs.jctc.2c00472 ↗
43. Choi, S., Semon, P., Kang, B., Kutepov, A. & Kotliar, G. ComDMFT: a massively parallel computer package for the electronic structure of correlated-electron systems. Comput. Phys. Commun. 244, 277–294 (2019).10.1016/j.cpc.2019.07.003 ↗
44. Singh, V. et al. DMFTwDFT: an open-source code combining Dynamical Mean Field Theory with various density functional theory packages. Comput. Phys. Commun. 261, 107778 (2021).10.1016/j.cpc.2020.107778 ↗
45. Merkel, M. E., Carta, A., Beck, S. & Hampel, A. solid_dmft: gray-boxing DFT+DMFT materials simulations with TRIQS. J. Open Source Software 7, 4623 (2022).10.21105/joss.04623 ↗
46. Gull, E. et al. Continuous-time Monte Carlo methods for quantum impurity models. Rev. Mod. Phys. 83, 349–404 (2011).10.1103/RevModPhys.83.349 ↗
47. Werner, P. & Millis, A. J. Hybridization expansion impurity solver: general formulation and application to Kondo lattice and two-orbital models. Phys. Rev. B 74, 155107 (2006).10.1103/PhysRevB.74.155107 ↗
48. Werner, P., Comanac, A., de’ Medici, L., Troyer, M. & Millis, A. J. Continuous-time solver for quantum impurity models. Phys. Rev. Lett. 97, 076405 (2006).10.1103/PhysRevLett.97.076405 ↗
49. Melnick, C. et al. Accelerated impurity solver for DMFT and its diagrammatic extensions. Comput. Phys. Commun. 267, 108075 (2021).10.1016/j.cpc.2021.108075 ↗
50. Koçer, C. P., Haule, K., Pascut, G. L. & Monserrat, B. Efficient lattice dynamics calculations for correlated materials with DFT + DMFT. Phys. Rev. B 102, 245104 (2020).10.1103/PhysRevB.102.245104 ↗
51. Abramovitch, D. J., Zhou, J.-J., Mravlje, J., Georges, A. & Bernardi, M. Combining electron-phonon and dynamical mean-field theory calculations of correlated materials: transport in the correlated metal Sr2RuO4. Phys. Rev. Mater. 7, 093801 (2023).10.1103/PhysRevMaterials.7.093801 ↗
52. Khanal, G. & Haule, K. Correlation driven phonon anomalies in bulk FeSe. Phys. Rev. B 102, 241108 (2020).10.1103/PhysRevB.102.241108 ↗
53. Aryasetiawan, F. & Gunnarsson, O. The GW method. Rep. Prog. Phys. 61, 237 (1998).10.1088/0034-4885/61/3/002 ↗
54. Boehnke, L., Nilsson, F., Aryasetiawan, F. & Werner, P. When strong correlations become weak: Consistent merging of GW and DMFT. Phys. Rev. B 94, 201106 (2016).10.1103/PhysRevB.94.201106 ↗
55. Zhu, T. & Chan, G. K.-L. Ab Initio Full Cell GW + DMFT for Correlated Materials. Phys. Rev. X 11, 021006 (2021).
56. Galler, A. et al. The AbinitioDΓA Project v1.0: Non-local correlations beyond and susceptibilities within dynamical mean-field theory. Comput. Phys. Commun. 245, 106847 (2019).10.1016/j.cpc.2019.07.012 ↗
57. Rohringer, G. et al. Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory. Rev. Mod. Phys. 90, 025003 (2018).10.1103/RevModPhys.90.025003 ↗
58. Toschi, A., Katanin, A. A. & Held, K. Dynamical vertex approximation: a step beyond dynamical mean-field theory. Phys. Rev. B 75, 045118 (2007).10.1103/PhysRevB.75.045118 ↗
59. Galler, A., Thunström, P., Gunacker, P., Tomczak, J. M. & Held, K. Ab initio dynamical vertex approximation. Phys. Rev. B 95, 115107 (2017).10.1103/PhysRevB.95.115107 ↗
60. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).10.1103/PhysRevB.59.1758 ↗
61. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).10.1103/PhysRevB.54.11169 ↗
62. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. 21, 395502 (2009).
63. Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys. 29, 465901 (2017).
64. Pizzi, G. et al. Wannier90 as a community code: new features and applications. J. Phys. 32, 165902 (2020).
65. He, R.-Q. & Lu, Z.-Y. Quantum renormalization groups based on natural orbitals. Phys. Rev. B 89, 085108 (2014).10.1103/PhysRevB.89.085108 ↗
66. He, R.-Q., Dai, J. & Lu, Z.-Y. Natural orbitals renormalization group approach to the two-impurity Kondo critical point. Phys. Rev. B 91, 155140 (2015).10.1103/PhysRevB.91.155140 ↗
67. Huang, L. et al. iQIST: an open source continuous-time quantum Monte Carlo impurity solver toolkit. Comput. Phys. Commun. 195, 140–160 (2015).10.1016/j.cpc.2015.04.020 ↗
68. Huang, L. iQIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit. Comput. Phys. Commun. 221, 423–424 (2017).10.1016/j.cpc.2017.08.026 ↗
69. Huang, L. ACFlow: An open source toolkit for analytic continuation of quantum Monte Carlo data. Comput. Phys. Commun. 292, 108863 (2023).10.1016/j.cpc.2023.108863 ↗
70. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).10.1103/PhysRevB.50.17953 ↗
71. Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847–12865 (1997).10.1103/PhysRevB.56.12847 ↗
72. Sakuma, R. Symmetry-adapted Wannier functions in the maximal localization procedure. Phys. Rev. B 87, 235109 (2013).10.1103/PhysRevB.87.235109 ↗
73. Lambin, P. & Vigneron, J. P. Computation of crystal Green’s functions in the complex-energy plane with the use of the analytical tetrahedron method. Phys. Rev. B 29, 3430–3437 (1984).10.1103/PhysRevB.29.3430 ↗
74. Amadon, B., Jollet, F. & Torrent, M. γ and β cerium: LDA + U calculations of ground-state parameters. Phys. Rev. B 77, 155104 (2008).10.1103/PhysRevB.77.155104 ↗
75. Ouyang, Z., Wang, J.-M., He, R.-Q. & Lu, Z.-Y. DFT+DMFT study of correlated electronic structure in the monolayer-trilayer phase of La3Ni2O7. Phys. Rev. B 111, 125111 (2025).10.1103/PhysRevB.111.125111 ↗
76. Sémon, P., Yee, C.-H., Haule, K. & Tremblay, A.-M. S. Lazy skip-lists: an algorithm for fast hybridization-expansion quantum Monte Carlo. Phys. Rev. B 90, 075149 (2014).10.1103/PhysRevB.90.075149 ↗
77. Boehnke, L., Hafermann, H., Ferrero, M., Lechermann, F. & Parcollet, O. Orthogonal polynomial representation of imaginary-time Green’s functions. Phys. Rev. B 84, 075145 (2011).10.1103/PhysRevB.84.075145 ↗
78. Shinaoka, H., Otsuki, J., Ohzeki, M. & Yoshimi, K. Compressing Green’s function using intermediate representation between imaginary-time and real-frequency domains. Phys. Rev. B 96, 035147 (2017).10.1103/PhysRevB.96.035147 ↗
79. Hafermann, H., Patton, K. R. & Werner, P. Improved estimators for the self-energy and vertex function in hybridization-expansion continuous-time quantum Monte Carlo simulations. Phys. Rev. B 85, 205106 (2012).10.1103/PhysRevB.85.205106 ↗
80. Jarrell, M. & Gubernatis, J. Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data. Phys. Rep. 269, 133–195 (1996).10.1016/0370-1573(95)00074-7 ↗
81. Fei, J., Yeh, C.-N. & Gull, E. Nevanlinna Analytical Continuation. Phys. Rev. Lett. 126, 056402 (2021).10.1103/PhysRevLett.126.056402 ↗
82. Sandvik, A. W. Stochastic method for analytic continuation of quantum Monte Carlo data. Phys. Rev. B 57, 10287–10290 (1998).10.1103/PhysRevB.57.10287 ↗
83. Shao, H. & Sandvik, A. W. Progress on stochastic analytic continuation of quantum Monte Carlo data. Phys. Rep. 1003, 1–88 (2023).10.1016/j.physrep.2022.11.002 ↗
84. Mishchenko, A. S., Prokof’ev, N. V., Sakamoto, A. & Svistunov, B. V. Diagrammatic quantum Monte Carlo study of the Fröhlich polaron. Phys. Rev. B 62, 6317–6336 (2000).10.1103/PhysRevB.62.6317 ↗
85. Huang, L. & Liang, S. Stochastic pole expansion method for analytic continuation of the Green’s function. Phys. Rev. B 108, 235143 (2023).10.1103/PhysRevB.108.235143 ↗
86. Huang, L. & Liang, S. Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation. Phys. Rev. D 109, 054508 (2024).10.1103/PhysRevD.109.054508 ↗
87. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10.1103/PhysRevLett.77.3865 ↗
88. Nekrasov, I. A. et al. Momentum-resolved spectral functions of SrVO3 calculated by LDA + DMFT. Phys. Rev. B 73, 155112 (2006).10.1103/PhysRevB.73.155112 ↗
89. Kuneš, J., Lukoyanov, A. V., Anisimov, V. I., Scalettar, R. T. & Pickett, W. E. Collapse of magnetic moment drives the Mott transition in MnO. Nat. Mater. 7, 198–202 (2008).10.1038/nmat2115 ↗
90. Ouyang, Z. et al. Hund electronic correlation in La3Ni2O7 under high pressure. Phys. Rev. B 109, 115114 (2024).10.1103/PhysRevB.109.115114 ↗
91. Chen, Y., Tian, Y.-H., Wang, J.-M., He, R.-Q. & Lu, Z.-Y. Non-Fermi liquid and antiferromagnetic correlations with hole doping in the bilayer two-orbital Hubbard model of La3Ni2O7 at zero temperature. Phys. Rev. B 110, 235119 (2024).10.1103/PhysRevB.110.235119 ↗
92. Rey, M. et al. Preparation and structure of the compounds SrVO3 and Sr2VO4. J. Solid State Chem. 86, 101–108 (1990).10.1016/0022-4596(90)90119-I ↗
93. Nekrasov, I. A. et al. Comparative study of correlation effects in CaVO3 and SrVO3. Phys. Rev. B 72, 155106 (2005).10.1103/PhysRevB.72.155106 ↗
94. Huang, L. & Wang, Y. Dynamical screening in strongly correlated metal SrVO3. Europhys. Lett. 99, 67003 (2012).10.1209/0295-5075/99/67003 ↗
95. Yoshida, T., Kobayashi, M., Yoshimatsu, K., Kumigashira, H. & Fujimori, A. Correlated electronic states of SrVO3 revealed by angle-resolved photoemission spectroscopy. J. Electron Spectros. Relat. Phenomena 208, 11–16 (2016).10.1016/j.elspec.2015.11.012 ↗
96. Sekiyama, A. et al. Mutual experimental and theoretical validation of bulk photoemission spectra of Sr1−xCaxVO3. Phys. Rev. Lett. 93, 156402 (2004).10.1103/PhysRevLett.93.156402 ↗
97. Sun, H. et al. Signatures of superconductivity near 80 K in a nickelate under high pressure. Nature 621, 493–498 (2023).10.1038/s41586-023-06408-7 ↗
98. Yang, J. et al. Orbital-dependent electron correlation in double-layer nickelate La3Ni2O7. Nat. Commun. 15, 4373 (2024).10.1038/s41467-024-48701-7 ↗
99. Cao, Y. & Yang, Y.-f Flat bands promoted by Hund’s rule coupling in the candidate double-layer high-temperature superconductor La3Ni2O7 under high pressure. Phys. Rev. B 109, L081105 (2024).10.1103/PhysRevB.109.L081105 ↗
100. Georges, A., Medici, L. D. & Mravlje, J. Strong correlations from Hund’s coupling. Annu. Rev. Condens. Matter Phys. 4, 137–178 (2013).10.1146/annurev-conmatphys-020911-125045 ↗