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Steady-state study of the nonequilibrium properties of SrVO3

Tommaso Maria Mazzocchi*, Markus Aichhorn, and Enrico Arrigoni†

  • *Contact author: mazzocchi@tugraz.at
  • †Contact author: arrigoni@tugraz.at
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Phys. Rev. B 114, 105138 – Published 25 August, 2026

DOI: https://doi.org/10.1103/svb6-63vj

Abstract

We present the mixed-configuration approximation (MCA) based on the auxiliary master equation approach impurity solver to study multiorbital correlated systems under equilibrium and nonequilibrium conditions within dynamical mean-field theory (DMFT). We benchmark the method for bulk and layered SrVO3 in equilibrium and apply it to a prototypical nonequilibrium geometry in which a voltage bias is applied perpendicular to the layer via reservoirs held at different chemical potentials. For bulk SrVO3, MCA reproduces the metallic state at moderate interaction strengths, but it overestimates the weight of the lower band relative to quantum Monte Carlo (QMC) and fork tensor product state (FTPS) solvers. With respect to QMC and FTPS, MCA yields an earlier metal-to-insulator transition as the electron-electron interaction is increased. In layered SrVO3 at equilibrium, MCA partially captures the orbital polarization in favor of the in-plane xy orbital, although not as strong as in the DMFT-converged results obtained with QMC. Finally, under applied bias, we observe a pronounced redistribution of orbital occupations, demonstrating that the method captures bias-driven orbital charge transfer in realistic materials in nonequilibrium conditions.

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References (61)

  1. C. Aron, Dielectric breakdown of a Mott insulator, Phys. Rev. B 86, 085127 (2012).
  2. A. Amaricci, C. Weber, M. Capone, and G. Kotliar, Approach to a stationary state in a driven Hubbard model coupled to a thermostat, Phys. Rev. B 86, 085110 (2012).
  3. Y. Murakami and P. Werner, Nonequilibrium steady states of electric field driven Mott insulators, Phys. Rev. B 98, 075102 (2018).
  4. T. M. Mazzocchi, P. Gazzaneo, J. Lotze, and E. Arrigoni, Correlated Mott insulators in strong electric fields: Role of phonons in heat dissipation, Phys. Rev. B 106, 125123 (2022).
  5. J. E. Han, C. Aron, X. Chen, I. Mansaray, J.-H. Han, K.-S. Kim, M. Randle, and J. P. Bird, Correlated insulator collapse due to quantum avalanche via in-gap ladder states, Nat. Commun. 14, 2936 (2023).
  6. E. Janod, J. Tranchant, B. Corraze, M. Querré, P. Stoliar, M. Rozenberg, T. Cren, D. Roditchev, V. T. Phuoc, M.-P. Besland, and L. Cario, Resistive switching in Mott insulators and correlated systems, Adv. Funct. Mater. 25, 6287 (2015).
  7. B. D. Hoskins, G. C. Adam, E. Strelcov, N. Zhitenev, A. Kolmakov, D. B. Strukov, and J. J. McClelland, Stateful characterization of resistive switching TiO2 with electron-beam-induced currents, Nat. Commun. 8, 1972 (2017).
  8. W. Sun, B. Gao, M. Chi, Q. Xia, J. J. Yang, H. Qian, and H. Wu, Understanding memristive switching via in situ characterization and device modeling, Nat. Commun. 10, 3453 (2019).
  9. Z. Zhong, M. Wallerberger, J. M. Tomczak, C. Taranto, N. Parragh, A. Toschi, G. Sangiovanni, and K. Held, Electronics with correlated oxides: SrVo3/SrTiO3 as a Mott transistor, Phys. Rev. Lett. 114, 246401 (2015).
  10. S. Bhandary, E. Assmann, M. Aichhorn, and K. Held, Charge self-consistency in density functional theory combined with dynamical mean field theory: k-space reoccupation and orbital order, Phys. Rev. B 94, 155131 (2016).
  11. T. M. Mazzocchi, D. Werner, M. Aichhorn, and E. Arrigoni, Mixed-configuration approximation for multiorbital systems out of equilibrium, Phys. Rev. B 112, 155127 (2025).
  12. A. Georges and G. Kotliar, Hubbard model in infinite dimensions, Phys. Rev. B 45, 6479 (1992).
  13. 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).
  14. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
  15. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  16. E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer, and P. Werner, Continuous – time Monte Carlo methods for quantum impurity models, Rev. Mod. Phys. 83, 349 (2011).
  17. P. Werner, A. Comanac, L. de' Medici, M. Troyer, and A. J. Millis, Continuous-time solver for quantum impurity models, Phys. Rev. Lett. 97, 076405 (2006).
  18. G. Cohen, E. Gull, D. R. Reichman, and A. J. Millis, Taming the dynamical sign problem in real-time evolution of quantum many-body problems, Phys. Rev. Lett. 115, 266802 (2015).
  19. A. E. Antipov, Q. Dong, J. Kleinhenz, G. Cohen, and E. Gull, Currents and Green's functions of impurities out of equilibrium: Results from inchworm quantum Monte Carlo, Phys. Rev. B 95, 085144 (2017).
  20. A. Erpenbeck, T. Blommel, L. Zhang, W.-T. Lin, G. Cohen, and E. Gull, Steady-state properties of multi-orbital systems using quantum Monte Carlo, J. Chem. Phys. 161, 094104 (2024).
  21. K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Rev. Mod. Phys. 47, 773 (1975).
  22. R. Bulla, T. A. Costi, and T. Pruschke, Numerical renormalization group method for quantum impurity systems, Rev. Mod. Phys. 80, 395 (2008).
  23. F. B. Anders, Steady-state currents through nanodevices: A scattering-states numerical renormalization-group approach to open quantum systems, Phys. Rev. Lett. 101, 066804 (2008).
  24. J. E. Han, Nonequilibrium statistics of a biased Kondo resonance, Phys. Rev. B 113, 045141 (2026).
  25. K. M. Stadler, A. K. Mitchell, J. von Delft, and A. Weichselbaum, Interleaved numerical renormalization group as an efficient multiband impurity solver, Phys. Rev. B 93, 235101 (2016).
  26. A. Horvat, R. Žitko, and J. Mravlje, Low-energy physics of three-orbital impurity model with Kanamori interaction, Phys. Rev. B 94, 165140 (2016).
  27. M. Caffarel and W. Krauth, Exact diagonalization approach to correlated fermions in infinite dimensions: Mott transition and superconductivity, Phys. Rev. Lett. 72, 1545 (1994).
  28. A. Dorda, M. Nuss, W. von der Linden, and E. Arrigoni, Auxiliary master equation approach to non – equilibrium correlated impurities, Phys. Rev. B 89, 165105 (2014).
  29. D. Werner, J. Lotze, and E. Arrigoni, Configuration interaction based nonequilibrium steady state impurity solver, Phys. Rev. B 107, 075119 (2023).
  30. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011).
  31. M. Grundner, F. B. Kugler, O. Parcollet, U. Schollwöck, A. Georges, and A. Hampel, LiV2O4: Hund-assisted orbital-selective Mottness, Phys. Rev. B 112, L041106 (2025).
  32. D. Bauernfeind, M. Zingl, R. Triebl, M. Aichhorn, and H. G. Evertz, Fork tensor-product states: Efficient multiorbital real-time DMFT solver, Phys. Rev. X 7, 031013 (2017).
  33. M. Nayak, J. Thoenniss, M. Sonner, D. A. Abanin, and P. Werner, Steady-state dynamical mean field theory based on influence functional matrix product states, Phys. Rev. B 112, 035103 (2025).
  34. M. Sonner, V. Link, and D. A. Abanin, Semigroup influence matrices for nonequilibrium quantum impurity models, Phys. Rev. Lett. 135, 170402 (2025).
  35. D. Bauernfeind, R. Triebl, M. Zingl, M. Aichhorn, and H. G. Evertz, Dynamical mean-field theory on the real-frequency axis: p−d hybridization and atomic physics in SrMnO3, Phys. Rev. B 97, 115156 (2018).
  36.  A configuration is defined as the collection of fixed occupation states of the configuration orbitals.
  37. As already argued in Ref. [11], any single-band impurity solver can be extended according to the prescription of the MCA scheme.
  38. M. E. Sorantin, A. Dorda, K. Held, and E. Arrigoni, Impact ionization processes in the steady state of a driven Mott-insulating layer coupled to metallic leads, Phys. Rev. B 97, 115113 (2018).
  39. P. Gazzaneo, T. M. Mazzocchi, J. Lotze, and E. Arrigoni, Impact ionization processes in a photodriven Mott insulator: Influence of phononic dissipation, Phys. Rev. B 106, 195140 (2022).
  40. T. M. Mazzocchi, D. Werner, P. Gazzaneo, and E. Arrigoni, Correlated Mott insulators in a strong electric field: The effects of phonon renormalization, Phys. Rev. B 107, 155103 (2023).
  41. P. Gazzaneo, D. Werner, T. M. Mazzocchi, and E. Arrigoni, Photodriven Mott insulating heterostructures: A steady-state study of impact ionization processes, Phys. Rev. B 109, 235134 (2024).
  42. F. Künzel, A. Erpenbeck, D. Werner, E. Arrigoni, E. Gull, G. Cohen, and M. Eckstein, Numerically exact simulation of photodoped Mott insulators, Phys. Rev. Lett. 132, 176501 (2024).
  43. Our notation is such that P¯ denotes conditional probability.
  44. The configuration tuple resulting by singling out only one target orbital lists all the remaining orbitals with their respective states. We point out that given the correction to the onsite energy in Eq. (8), the order of the orbitals in the configuration does not matter.
  45. Notice that solving Eq. (17) is equivalent to finding the eigenvector corresponding to the eigenvalue 1 of the matrix (18). The existence of one such eigenvalue is guaranteed by the column stochastic nature of the conditional probability matrices, see Ref. [11]. Resorting to the fixed-point method, i.e., iterating Eq. (17) until the probability vector does not change any longer, constitutes a more stable and versatile option than solving the eigenvalue problem, especially in (quasi) degenerate systems.
  46. H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, and P. Werner, Nonequilibrium dynamical mean-field theory and its applications, Rev. Mod. Phys. 86, 779 (2014).
  47. O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko, L. Messio, and P. Seth, TRIQS: A toolbox for research on interacting quantum systems, Comput. Phys. Commun. 196, 398 (2015).
  48. P. Seth, I. Krivenko, M. Ferrero, and O. Parcollet, TRIQS/CTHYB: A continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impurity problems, Comput. Phys. Commun. 200, 274 (2016).
  49. P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. H. Madsen, and L. D. Marks, WIEN2k: An APW+lo program for calculating the properties of solids, J. Chem. Phys. 152, 074101 (2020).
  50. M. Aichhorn, L. Pourovskii, P. Seth, V. Vildosola, M. Zingl, O. E. Peil, X. Deng, J. Mravlje, G. J. Kraberger, C. Martins, M. Ferrero, and O. Parcollet, TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials, Comput. Phys. Commun. 204, 200 (2016).
  51. G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Ibañez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
  52. A. Liebsch, Surface versus bulk Coulomb correlations in photoemission spectra of SrVO3 and CaVO3, Phys. Rev. Lett. 90, 096401 (2003).
  53. A. Sekiyama, H. Fujiwara, S. Imada, S. Suga, H. Eisaki, S. I. Uchida, K. Takegahara, H. Harima, Y. Saitoh, I. A. Nekrasov, G. Keller, D. E. Kondakov, A. V. Kozhevnikov, T. Pruschke, K. Held, D. Vollhardt, and V. I. Anisimov, Mutual experimental and theoretical validation of bulk photoemission spectra of Sr1−xCaxVO3, Phys. Rev. Lett. 93, 156402 (2004).
  54. O. Parcollet, G. Biroli, and G. Kotliar, Cluster dynamical mean field analysis of the Mott transition, Phys. Rev. Lett. 92, 226402 (2004).
  55. I. A. Nekrasov, G. Keller, D. E. Kondakov, A. V. Kozhevnikov, T. Pruschke, K. Held, D. Vollhardt, and V. I. Anisimov, Comparative study of correlation effects in CaVo3 and SrVo3, Phys. Rev. B 72, 155106 (2005).
  56. I. A. Nekrasov, K. Held, G. Keller, D. E. Kondakov, T. Pruschke, M. Kollar, O. K. Andersen, V. I. Anisimov, and D. Vollhardt, Momentum-resolved spectral functions of SrVO3 calculated by LDA + DMFT, Phys. Rev. B 73, 155112 (2006).
  57. Y. Nomura, M. Kaltak, K. Nakamura, C. Taranto, S. Sakai, A. Toschi, R. Arita, K. Held, G. Kresse, and M. Imada, Effective on-site interaction for dynamical mean-field theory, Phys. Rev. B 86, 085117 (2012).
  58. We note that the AMEA impurity solver has a finite energy resolution, which can lead to small numerical deviations from an exact Fermi distribution already at equilibrium and thus to a slight offset in the filling from the nominal value of 1/6. Under nonequilibrium conditions, where the Keldysh component of the hybridization function acquires a nontrivial frequency dependence due to the application of a finite bias Φ, these deviations may become more pronounced. As a consequence, the total occupation (per spin) can lie marginally above its nominal value even for biases Φ well within the gap, i.e., in a regime where physical charge injection is expected to be negligible.
  59. R. Kubo, Generalized cumulant expansion method, J. Phys. Soc. Jpn. 17, 1100 (1962).
  60. W. J. Shugard and J. D. Weeks, Renormalized finite-cluster method for lattice models. I. Site renormalization and star cluster expansions, Phys. Rev. B 22, 5245 (1980).
  61. https://doi.org/10.3217/snf77-2hv59.

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Phys. Rev. B 114, 105138– Published 25 August, 2026
  • Received 6 February 2026
  • Revised 10 August 2026
  • Accepted 13 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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