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Linear Foundation Model for Quantum Embedding: Data-Driven Compression of the Ghost Gutzwiller Variational Space

Samuele Giuli1, Hasanat Hasan2,3, Benedikt Kloss1, Marius S. Frank4, Tsung-Han Lee5, Olivier Gingras1,6, Yong-Xin Yao7,8,*, and Nicola Lanatà2,1,†

  • *Contact author: ykent@iastate.edu
  • †Contact author: nxlsps@rit.edu
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PRX Intelligence 1, 013001 – Published 28 July, 2026

DOI: https://doi.org/10.1103/phk3-pvhm

Abstract

Simulations of quantum matter rely mainly on Kohn-Sham density functional theory (DFT), which often fails for strongly correlated systems. Quantum embedding (QE) theories address this limitation by mapping the system onto an auxiliary embedding Hamiltonian (EH) describing fragment-environment interactions, but the EH is typically large and its iterative solution is the primary computational bottleneck. We introduce a linear foundation model for QE that utilizes principal component analysis to compress the space of quantum states needed to solve the EH within a small variational subspace. Using a data-driven active-learning scheme, we learn this subspace from EH ground states and reduce each embedding solution to a deterministic ground-state eigenvalue problem in the reduced space. Within the ghost-Gutzwiller approximation, we show for a three-orbital Hubbard model that a variational space learned on a Bethe lattice is transferable to square and cubic lattices without additional training, while substantially reducing the cost of the EH step. We further validate the approach on plutonium, where a single variational space reproduces the energetics of all six crystalline phases while reducing the cost of the EH solution by orders of magnitude. This provides a practical route to overcome the main computational bottleneck of QE frameworks, paving the way for high-throughput ab initio simulations of strongly correlated materials at a near-DFT cost.

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References (102)

  1. Materials genome initiative for global competitiveness, National Science and Technology Council (U.S.) (2011), available at: https://www.mgi.gov/sites/mgi/files/materials_genome_initiative-final.pdf.
  2. L.-Q. Chen, L.-D. Chen, S. V. Kalinin, G. Klimeck, S. K. Kumar, J. Neugebauer, and I. Terasaki, Design and discovery of materials guided by theory and computation, npj Comput. Mater. 1, 15007 (2015).
  3. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
  4. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  5. P. R. C. Kent and G. Kotliar, Toward a predictive theory of correlated materials, Science 361, 348 (2018).
  6. N. F. Mott, Metal-Insulator Transitions, 2nd ed. (Taylor & Francis, London, 1990).
  7. J. A. Schiller, L. K. Wagner, and E. Ertekin, Phase stability and properties of manganese oxide polymorphs: Assessment and insights from diffusion Monte Carlo, Phys. Rev. B 92, 235209 (2015).
  8. H. Peng and S. Lany, Polymorphic energy ordering of MgO, ZnO, GaN, and MnO within the random phase approximation, Phys. Rev. B 87, 174113 (2013).
  9. A. Schrön, C. Rödl, and F. Bechstedt, Energetic stability and magnetic properties of MnO in the rocksalt, wurtzite, and zinc-blende structures: Influence of exchange and correlation, Phys. Rev. B 82, 165109 (2010).
  10. J. Kolorenč and L. Mitas, Quantum Monte Carlo calculations of structural properties of FeO under pressure, Phys. Rev. Lett. 101, 185502 (2008).
  11. I. Leonov, L. Pourovskii, A. Georges, and I. A. Abrikosov, Magnetic collapse and the behavior of transition metal oxides at high pressure, Phys. Rev. B 94, 155135 (2016).
  12. K. Haule, Structural predictions for correlated electron materials using the functional dynamical mean field theory approach, J. Phys. Soc. Jpn. 87, 041005 (2018).
  13. N. Lanatà, T.-H. Lee, Y.-X. Yao, V. Stevanović, and V. Dobrosavljević, Connection between Mott physics and crystal structure in a series of transition metal binary compounds, npj Comput. Mater. 5, 30 (2019).
  14. J. N. Cross, T.-H. Lee, C.-J. Kang, Y.-X. Yao, S. K. Cary, J. T. Stritzinger, M. J. Polinski, C. D. McKinley, T. E. Albrecht-Schmitt, and N. Lanatà, Origins of the odd optical observables in plutonium and americium tungstates, Chem. Sci. 10, 6508 (2019).
  15. S. S. Galley, A. A. Arico, T.-H. Lee, X. Deng, Y.-X. Yao, J. M. Sperling, V. Proust, J. S. Storbeck, V. Dobrosavljevic, J. N. Neu, T. Siegrist, R. E. Baumbach, T. E. Albrecht-Schmitt, N. Kaltsoyannis, and N. Lanatà, Uncovering the origin of divergence in the CsM(CrO4)2 (M = La, Pr, Nd, Sm, Eu; Am) family through the chemical bonding in a molecular cluster and by band structure analysis, J. Am. Chem. Soc. 140, 1674 (2018).
  16. P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006).
  17. P. Johnpierre and R. L. Greene, High-temperature superconductivity in iron-based materials, Nat. Phys. 6, 645 (2010).
  18. M. Yi, Y. Zhang, Z.-X. Shen, and D. Lu, Role of the orbital degree of freedom in iron-based superconductors, npj Comput. Mater. 2, 57 (2017).
  19. L. Miao, R. Basak, S. Ran, Y. Xu, E. Kotta, H. He, J. D. Denlinger, Y.-D. Chuang, Y. Zhao, Z. Xu, J. W. Lynn, J. R. Jeffries, S. R. Saha, I. Giannakis, P. Aynajian, C.-J. Kang, Y. Wang, G. Kotliar, N. P. Butch, and L. A. Wray, High temperature singlet-based magnetism from Hund's rule correlations, Nat. Commun. 10, 644 (2019).
  20. E. M. Nica, R. Yu, and Q. Si, Orbital-selective pairing and superconductivity in iron selenides, npj Comput. Mater. 2, 24 (2017).
  21. P. Dai, J. Hu, and E. Dagotto, Magnetism and its microscopic origin in iron-based high-temperature superconductors, Nat. Phys. 8, 709 (2012).
  22. J.-F. Ge, Z.-L. Liu, C. Liu, C.-L. Gao, D. Qian, Q.-K. Xue, Y. Liu, and J.-F. Jia, Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3, Nat. Mater. 14, 285 (2015).
  23. S. Manna, A. Kamlapure, L. Cornils, T. Hänke, E. M. J. Hedegaard, M. Bremholm, B. B. Iversen, P. Hofmann, J. Wiebe, and R. Wiesendanger, Interfacial superconductivity in a bi-collinear antiferromagnetically ordered FeTe monolayer on a topological insulator, Nat. Commun. 8, 14074 (2017).
  24. V. Anisimov and Y. Izyumov, Electronic Structure of Strongly Correlated Materials (Springer, Berlin, 2010).
  25. V. I. Anisimov, A. I. Oteryaev, M. A. Korotin, A. O. Anokhin, and G. Kotliar, First-principles calculations of the electronic structure and spectra of strongly correlated systems: Dynamical mean-field theory, J. Phys.: Condens. Matter 9, 7359 (1997).
  26. K. Held, A. Nekrasov, G. Keller, V. Eyert, N. Blümer, A. K. McMahan, R. T. Scalettar, Th. Pruschke, V. I. Anisimov, and D. Vollhardt, Realistic investigations of correlated electron systems with LDA + DMFT, Phys. Status Solidi (B) 243, 2599 (2006).
  27. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13 (1996).
  28. J.-Z. Zhao, J.-N. Zhuang, X.-Y. Deng, Y. Bi, L.-C. Cai, Z. Fang, and X. Dai, Implementation of LDA + DMFT with the pseudo-potential-plane-wave method, Chin. Phys. B 21, 057106 (2012).
  29. G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Electronic structure calculations with dynamical mean-field theory, Rev. Mod. Phys. 78, 865 (2006).
  30. G. Knizia and G. K.-L. Chan, Density matrix embedding: A simple alternative to dynamical mean-field theory, Phys. Rev. Lett. 109, 186404 (2012).
  31. G. H. Booth and G. K.-L. Chan, Spectral functions of strongly correlated extended systems via an exact quantum embedding, Phys. Rev. B 91, 155107 (2015).
  32. F. Lechermann, A. Georges, G. Kotliar, and O. Parcollet, Rotationally invariant slave-boson formalism and momentum dependence of the quasiparticle weight, Phys. Rev. B 76, 155102 (2007).
  33. T. Li, P. Wölfle, and P. J. Hirschfeld, Spin-rotation-invariant slave-boson approach to the Hubbard model, Phys. Rev. B 40, 6817 (1989).
  34. N. Lanatà, Y. Yao, X. Deng, V. Dobrosavljević, and G. Kotliar, Slave boson theory of orbital differentiation with crystal field effects: Application to UO2, Phys. Rev. Lett. 118, 126401 (2017).
  35. M. C. Gutzwiller, Correlation of electrons in a narrow s band, Phys. Rev. 137, A1726 (1965).
  36. N. Lanatà, Y. X. Yao, C.-Z. Wang, K.-M. Ho, and G. Kotliar, Phase diagram and electronic structure of praseodymium and plutonium, Phys. Rev. X 5, 011008 (2015).
  37. N. Lanatà, P. Barone, and M. Fabrizio, Fermi-surface evolution across the magnetic phase transition in the Kondo lattice model, Phys. Rev. B 78, 155127 (2008).
  38. W. Metzner and D. Vollhardt, Correlated lattice Fermions in d=∞ dimensions, Phys. Rev. Lett. 62, 324 (1989).
  39. X.-Y. Deng, L. Wang, X. Dai, and Z. Fang, Local density approximation combined with Gutzwiller method for correlated electron systems: Formalism and applications, Phys. Rev. B 79, 075114 (2009).
  40. K. M. Ho, J. Schmalian, and C. Z. Wang, Gutzwiller density functional theory for correlated electron systems, Phys. Rev. B 77, 073101 (2008).
  41. N. Lanatà, H. U. R. Strand, X. Dai, and B. Hellsing, Efficient implementation of the Gutzwiller variational method, Phys. Rev. B 85, 035133 (2012).
  42. J. Bünemann, F. Gebhard, T. Ohm, S. Weiser, and W. Weber, Gutzwiller-correlated wave functions: Application to ferromagnetic nickel, in Frontiers in Magnetic Materials, edited by A. V. Narlikar (Springer, Berlin, 2005), p. 117.
  43. C. Attaccalite and M. Fabrizio, Properties of Gutzwiller wave functions for multiband models, Phys. Rev. B 68, 155117 (2003).
  44. N. Lanatà, T.-H. Lee, Y.-X. Yao, and V. Dobrosavljević, Emergent Bloch excitations in Mott matter, Phys. Rev. B 96, 195126 (2017).
  45. M. S. Frank, T.-H. Lee, G. Bhattacharyya, P. K. H. Tsang, V. L. Quito, V. Dobrosavljević, O. Christiansen, and N. Lanatà, Quantum embedding description of the Anderson lattice model with the ghost Gutzwiller approximation, Phys. Rev. B 104, L081103 (2021).
  46. N. Lanatà, Operatorial formulation of the ghost rotationally invariant slave-boson theory, Phys. Rev. B 105, 045111 (2022).
  47. N. Lanatà, Derivation of the ghost Gutzwiller approximation from quantum embedding principles: Ghost density matrix embedding theory, Phys. Rev. B 108, 235112 (2023).
  48. L.-F. Arsenault, A. Lopez-Bezanilla, O. A. von Lilienfeld, and A. J. Millis, Machine learning for many-body physics: The case of the Anderson impurity model, Phys. Rev. B 90, 155136 (2014).
  49. E. Sheridan, C. Rhodes, F. Jamet, I. Rungger, and C. Weber, Data-driven dynamical mean-field theory: An error-correction approach to solve the quantum many-body problem using machine learning, Phys. Rev. B 104, 205120 (2021).
  50. E. J. Sturm, M. R. Carbone, D. Lu, A. Weichselbaum, and R. M. Konik, Predicting impurity spectral functions using machine learning, Phys. Rev. B 103, 245118 (2021).
  51. X.-Y. Ren, R.-S. Han, and L. Chen, Learning impurity spectral functions from density of states, J. Phys.: Condens. Matter 33, 495601 (2021).
  52. C. Venturella, C. Hillenbrand, J. Li, and T. Zhu, Machine learning many-body Green's functions for molecular excitation spectra, J. Chem. Theory Comput. 20, 143 (2024).
  53. E. Agapov, O. Bertomeu, A. Carballo, C. B. Mendl, and A. Sander, Predicting interacting Green's functions with neural networks, arXiv:2411.13644.
  54. F. Deng, Y. Lu, X. Cao, and Z. Zhong, Neural network impurity solver for real-frequency dynamical mean-field theory, arXiv:2511.14505.
  55. H. Lee, Z. Zhao, G. H. Booth, W. Ge, and C. Weber, Language-inspired machine learning approach for solving strongly correlated problems with dynamical mean-field theory, Phys. Rev. B 112, 035165 (2025).
  56. X. Dong, E. Gull, and L. Wang, Equivariant neural network for Green's functions of molecules and materials, Phys. Rev. B 109, 075112 (2024).
  57. P. Mitra and H. Banerjee, Deep learning-based prediction of self-energies from ab initio dynamical mean-field theory for real materials with minimal data sets, ChemRxiv, https://doi.org/10.26434/chemrxiv-2025-dp7rd.
  58. J. Rogers, T.-H. Lee, S. Pakdel, W. Xu, V. Dobrosavljević, Y.-X. Yao, O. Christiansen, and N. Lanatà, Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning, Phys. Rev. Res. 3, 013101 (2021).
  59. M. S. Frank, D. G. Artiukhin, T.-H. Lee, Y. Yao, K. Barros, O. Christiansen, and N. Lanatà, Active learning approach to simulations of strongly correlated matter with the ghost Gutzwiller approximation, Phys. Rev. Res. 6, 013242 (2024).
  60. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).
  61. H. Zhai, H. R. Larsson, S. Lee, Z.-H. Cui, T. Zhu, C. Sung, L. Peng, R. Peng, K. Liao, J. Tölle, J. Yang, S. Li, and G. K.-L. Chan, Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond, J. Chem. Phys. 159, 234801 (2023).
  62. U. Schollwöck, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005).
  63. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  64. S. R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48, 10345 (1993).
  65. X. Cao, Y. Lu, P. Hansmann, and M. W. Haverkort, Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr2RuO4, Phys. Rev. B 104, 115119 (2021).
  66. S. Boutin and B. Bauer, Quantum impurity models using superpositions of fermionic Gaussian states: Practical methods and applications, Phys. Rev. Res. 3, 033188 (2021).
  67. A.-K. Wu, B. Kloss, W. Krinitsin, M. T. Fishman, J. H. Pixley, and E. M. Stoudenmire, Disentangling interacting systems with fermionic Gaussian circuits: Application to quantum impurity models, Phys. Rev. B 111, 035119 (2025).
  68. P. V. Sriluckshmy, F. Jamet, and F. Šimkovic IV, Quantum assisted ghost Gutzwiller ansatz, arXiv:2506.21431.
  69. N. Gomes, A. Mukherjee, F. Zhang, T. Iadecola, C.-Z. Wang, K.-M. Ho, P. P. Orth, and Y.-X. Yao, Adaptive variational quantum imaginary time evolution approach for ground state preparation, Adv. Quantum Technol. 4, 2100114 (2021).
  70. T. Jiang, J. Rogers, M. S. Frank, O. Christiansen, Y.-X. Yao, and N. Lanatà, Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning, Phys. Rev. Res. 6, 033069 (2024).
  71. I.-C. Chen, A. Khindanov, C. M. Salazar, H. M. Barona, G. Harrabi, F. Zhang, C.-Z. Wang, T. Iadecola, N. Lanatà, and Y.-X. Yao, Quantum-classical embedding via ghost Gutzwiller approximation for enhanced simulations of correlated electron systems, npj Quantum Inf. (2026), doi:10.1038/s41534-026-01244-9.
  72. T.-H. Lee, N. Lanatà, and G. Kotliar, Accuracy of ghost rotationally invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size, Phys. Rev. B 107, L121104 (2023).
  73. T.-H. Lee, C. Melnick, R. Adler, N. Lanatà, and G. Kotliar, Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials, Phys. Rev. B 108, 245147 (2023).
  74. T.-H. Lee, C. Melnick, R. Adler, X. Sun, Y. Yao, N. Lanatà, and G. Kotliar, Charge self-consistent density functional theory plus ghost rotationally invariant slave-boson theory for correlated materials, Phys. Rev. B 110, 115126 (2024).
  75. V. I. Anisimov, F. Aryasetiawan, and A. I. Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: The LDA + U method, J. Phys.: Condens. Matter 9, 767 (1997).
  76. A. J. Kim, P. Werner, and R. Valentí, Alleviating the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multiorbital Hubbard models, Phys. Rev. B 101, 045108 (2020).
  77. R. Levy and B. K. Clark, Mitigating the sign problem through basis rotations, Phys. Rev. Lett. 126, 216401 (2021).
  78. S. Giuli, C. Mejuto-Zaera, and M. Capone, Altermagnetism from interaction-driven itinerant magnetism, Phys. Rev. B 111, L020401 (2025).
  79. D. Guerci, M. Capone, and M. Fabrizio, Exciton Mott transition revisited, Phys. Rev. Mater. 3, 054605 (2019).
  80. C. Mejuto-Zaera and M. Fabrizio, Efficient computational screening of strongly correlated materials: Multiorbital phenomenology within the ghost Gutzwiller approximation, Phys. Rev. B 107, 235150 (2023).
  81. A. M. Tagliente, C. Mejuto-Zaera, and M. Fabrizio, Revealing spinons by proximity effect, Phys. Rev. B 111, 125110 (2025).
  82. C. Mejuto-Zaera, Quantum embedding for molecules using auxiliary particles—The ghost Gutzwiller ansatz, Faraday Discuss. 254, 653 (2024).
  83. I. Pasqua, A. M. Tagliente, G. Bellomia, B. Monserrat, M. Fabrizio, and C. Mejuto-Zaera, Quasiparticle band picture bridging topology and strong correlations across energy scales, Phys. Rev. B 113, 155133 (2026).
  84. A. Cao, V. J. Bukas, V. Shadravan, Z. Wang, H. Li, J. Kibsgaard, I. Chorkendorff, and J. K. Nørskov, A spin promotion effect in catalytic ammonia synthesis, Nat. Commun. 13, 2382 (2022).
  85. K. Zhang, A. Cao, L. H. Wandall, J. Vernieres, J. Kibsgaard, J. K. Nørskov, and I. Chorkendorff, Spin-mediated promotion of Co catalysts for ammonia synthesis, Science 383, 1357 (2024).
  86. A. J. Coleman, Structure of fermion density matrices, Rev. Mod. Phys. 35, 668 (1963).
  87. D. Frame, R. He, I. Ipsen, D. Lee, D. Lee, and E. Rrapaj, Eigenvector continuation with subspace learning, Phys. Rev. Lett. 121, 032501 (2018).
  88. Y. Rath and G. H. Booth, Interpolating numerically exact many-body wave functions for accelerated molecular dynamics, Nat. Commun. 16, 2005 (2025).
  89. K. Atalar, Y. Rath, R. Crespo-Otero, and G. H. Booth, Fast and accurate nonadiabatic molecular dynamics enabled through variational interpolation of correlated electron wavefunctions, Faraday Discuss. 254, 542 (2024).
  90. N. Hogan, E. Kökcü, T. Steckmann, L. P. Doak, C. Mejuto-Zaera, D. Camps, R. V. Beeumen, W. A. de Jong, and A. F. Kemper, Efficient quantum implementation of dynamical mean field theory for correlated materials, arXiv:2508.05738.
  91. C. Mejuto-Zaera and A. F. Kemper, Quantum eigenvector continuation for chemistry applications, Electron. Struct. 5, 045007 (2023).
  92. T. Duguet, A. Ekström, R. J. Furnstahl, S. König, and D. Lee, Colloquium: Eigenvector continuation and projection-based emulators, Rev. Mod. Phys. 96, 031002 (2024).
  93. R. Rende, L. L. Viteritti, F. Becca, A. Scardicchio, A. Laio, and G. Carleo, Foundation neural-networks quantum states as a unified ansatz for multiple Hamiltonians, Nat. Commun. 16, 7213 (2025).
  94. Z. Zhouyin, T.-H. Lee, A. Chen, N. Lanatà, and H. Guo, Neural-quantum-states impurity solver for quantum embedding problems, Phys. Rev. B 113, 155123 (2026).
  95. H. Ma, H. Shang, and J. Yang, Quantum embedding method with transformer neural network quantum states for strongly correlated materials, npj Comput. Mater. 10, 220 (2024).
  96. P. W. Anderson, Infrared catastrophe in Fermi gases with local scattering potentials, Phys. Rev. Lett. 18, 1049 (1967).
  97. J. Kanamori, Electron correlation and ferromagnetism of transition metals, Prog. Theor. Phys. 30, 275 (1963).
  98. A. Georges, L. de’ Medici, and J. Mravlje, Strong correlations from Hund's coupling, Annu. Rev. Condens. Matter Phys. 4, 137 (2013).
  99. A. E. A. Allen, N. Lubbers, S. Matin, J. S. Smith, R. A. Messerly, S. Tretiak, and K. Barros, Learning together: Towards foundation models for machine learning interatomic potentials with meta-learning, npj Comput. Mater. 10, 154 (2024).
  100. J. Kim, J. Kim, J. Kim, J. Lee, Y. Park, Y. Kang, and S. Han, Data-efficient multifidelity training for high-fidelity machine learning interatomic potentials, J. Am. Chem. Soc. 147, 1042 (2025).
  101. S. Ju, J. You, G. Kim, Y. Park, H. An, and S. Han, Application of pretrained universal machine-learning interatomic potential for physicochemical simulation of liquid electrolytes in Li-ion batteries, Digit. Discov. 4, 1544 (2025).
  102. S. Giuli, PCA-gGA-data: Data and plotting scripts for “Linear foundation model for quantum embedding: Data-driven compression of the ghost Gutzwiller variational space” (v1.0), Zenodo (2026), doi: 10.5281/zenodo.19632781.

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PRX Intelligence 1, 013001– Published 28 July, 2026
  • Received 5 January 2026
  • Accepted 24 April 2026
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