Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Effective Enhancement of the Electron-Phonon Coupling Driven by Nonperturbative Electronic Density Fluctuations

E. Moghadas1, M. Reitner1, T. Wehling2, G. Sangiovanni3, S. Ciuchi4, and A. Toschi1

  • 1Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria
  • 2I. Institute for Theoretical Physics, Universität Hamburg, Notkestraße 9–11, 22607 Hamburg, Germany
  • 3Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ctd.qmat, Universität Würzburg, 97074 Würzburg, Germany
  • 4Dipartimento di Scienze Fisiche e Chimiche, Università dell’Aquila, Coppito-L’Aquila, Italy

Phys. Rev. Lett. 136, 126502 – Published 25 March, 2026

DOI: https://doi.org/10.1103/ld8v-qpf8

Abstract

We present a dynamical mean-field study of nonperturbative electronic mechanisms, which may lead to significant enhancements of the electron-phonon coupling in correlated electron systems. Analyzing the effects of electronic correlations on the lowest-order electron-phonon processes, we show that in the proximity of the Mott metal-to-insulator transition of the doped square lattice Hubbard model, where the isothermal charge response becomes particularly large at small momenta, the coupling of electrons to the lattice is strongly increased. This, in turn, induces significant corrections to both the electronic self-energy and phonon-mediated pairing interaction, indicating the possible onset of a strong interplay between lattice and electronic degrees of freedom even for small values of the bare electron-phonon coupling.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (112)

  1. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover Publications, Inc., New York, 2012).
  2. G. Rickayzen, Green’s Functions and Condensed Matter, Dover Books on Physics (Dover, New York, 2013).
  3. G. D. Mahan, Many-Particle Physics (Springer Science & Business Media, New York, 2013).
  4. M. Tinkham, Introduction to Superconductivity, 2nd ed. (Dover, Mineola, NY, 2004).
  5. P.-G. de Gennes, Superconductivity of Metals and Alloys, Revised ed. (Westview Press, Boulder, CO, 1999).
  6. J. A. Flores-Livas, L. Boeri, A. Sanna, G. Profeta, R. Arita, and M. Eremets, A perspective on conventional high-temperature superconductors at high pressure: Methods and materials, Phys. Rep. 856, 1 (2020).
  7. M. I. Eremets, V. S. Minkov, A. P. Drozdov, and P. P. Kong, The characterization of superconductivity under high pressure, Nat. Mater. 23, 26 (2024).
  8. L. Boeri, O. V. Dolgov, and A. A. Golubov, Is LaFeAsO1−xFx an electron-phonon superconductor?, Phys. Rev. Lett. 101, 026403 (2008).
  9. F. Giustino, Electron-phonon interactions from first principles, Rev. Mod. Phys. 89, 015003 (2017).
  10. M. Grilli and C. Castellani, Electron-phonon interactions in the presence of strong correlations, Phys. Rev. B 50, 16880 (1994).
  11. L. Pietronero, S. Strässler, and C. Grimaldi, Nonadiabatic superconductivity. I. Vertex corrections for the electron-phonon interactions, Phys. Rev. B 52, 10516 (1995).
  12. Z. B. Huang, W. Hanke, E. Arrigoni, and D. J. Scalapino, Electron-phonon vertex in the two-dimensional one-band Hubbard model, Phys. Rev. B 68, 220507(R) (2003).
  13. E. Koch and R. Zeyher, Renormalization of the electron-phonon coupling in the one-band Hubbard model, Phys. Rev. B 70, 094510 (2004).
  14. E. Cappelluti, B. Cerruti, and L. Pietronero, Charge fluctuations and electron-phonon interaction in the finite-U Hubbard model, Phys. Rev. B 69, 161101(R) (2004).
  15. O. Rösch and O. Gunnarsson, Apparent electron-phonon interaction in strongly correlated systems, Phys. Rev. Lett. 93, 237001 (2004).
  16. G. Sangiovanni, M. Capone, C. Castellani, and M. Grilli, Electron-phonon interaction close to a Mott transition, Phys. Rev. Lett. 94, 026401 (2005).
  17. G. Sangiovanni, O. Gunnarsson, E. Koch, C. Castellani, and M. Capone, Electron-phonon interaction and antiferromagnetic correlations, Phys. Rev. Lett. 97, 046404 (2006).
  18. G. Sangiovanni, M. Capone, and C. Castellani, Relevance of phonon dynamics in strongly correlated systems coupled to phonons: Dynamical mean-field theory analysis, Phys. Rev. B 73, 165123 (2006).
  19. A. Di Ciolo, J. Lorenzana, M. Grilli, and G. Seibold, Charge instabilities and electron-phonon interaction in the Hubbard-Holstein model, Phys. Rev. B 79, 085101 (2009).
  20. O. Rösch, G. Sangiovanni, and O. Gunnarsson, Sum rules and vertex corrections for electron-phonon interactions, Phys. Rev. B 75, 035119 (2007).
  21. O. Gunnarsson and O. Rösch, Interplay between electron–phonon and Coulomb interactions in cuprates, J. Phys. Condens. Matter 20, 043201 (2008).
  22. M. Capone, C. Castellani, and M. Grilli, Electron-phonon interaction in strongly correlated systems, Adv. Condens. Matter Phys. 2010, 920860 (2010).
  23. Z. Chen, Y. Wang, S. N. Rebec, T. Jia, M. Hashimoto, D. Lu, B. Moritz, R. G. Moore, T. P. Devereaux, and Z.-X. Shen, Anomalously strong near-neighbor attraction in doped 1d cuprate chains, Science 373, 1235 (2021).
  24. Y. Wang, Z. Chen, T. Shi, B. Moritz, Z.-X. Shen, and T. P. Devereaux, Phonon-mediated long-range attractive interaction in one-dimensional cuprates, Phys. Rev. Lett. 127, 197003 (2021).
  25. M. Jiang, Enhancing d-wave superconductivity with nearest-neighbor attraction in the extended Hubbard model, Phys. Rev. B 105, 024510 (2022).
  26. Z. Shen, J. Liu, H.-X. Wang, and Y. Wang, Signatures of the attractive interaction in spin spectra of one-dimensional cuprate chains, Phys. Rev. Res. 6, L032068 (2024).
  27. V. Velasco, G. Midei, M. Capone, and A. Perali, Pairing amplification induced by nonadiabatic effects on the electron-phonon interaction throughout the BCS-BEC crossover, Phys. Rev. B 111, 064512 (2025).
  28. D. J. Abramovitch, J. Coulter, S. Beck, and A. Millis, Electron-phonon coupling in correlated metals: A dynamical mean-field theory study, Phys. Rev. B 112, 075113 (2025).
  29. J. Coulter and A. J. Millis, Electron-phonon coupling in correlated materials: Insights from the Hubbard-Holstein model, arXiv:2505.08081.
  30. J. Hubbard, Electron correlations in narrow energy bands, Proc. R. Soc. A 276, 238 (1963).
  31. M. Qin, T. Schäfer, S. Andergassen, P. Corboz, and E. Gull, The Hubbard model: A computational perspective, Annu. Rev. Condens. Matter Phys. 13, 275 (2022).
  32. T. Schäfer, G. Rohringer, O. Gunnarsson, S. Ciuchi, G. Sangiovanni, and A. Toschi, Divergent precursors of the Mott-Hubbard transition at the two-particle level, Phys. Rev. Lett. 110, 246405 (2013).
  33. T. Schäfer, S. Ciuchi, M. Wallerberger, P. Thunström, O. Gunnarsson, G. Sangiovanni, G. Rohringer, and A. Toschi, Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint, Phys. Rev. B 94, 235108 (2016).
  34. O. Gunnarsson, G. Rohringer, T. Schäfer, G. Sangiovanni, and A. Toschi, Breakdown of traditional many-body theories for correlated electrons, Phys. Rev. Lett. 119, 056402 (2017).
  35. P. Chalupa, P. Gunacker, T. Schäfer, K. Held, and A. Toschi, Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson impurity model, Phys. Rev. B 97, 245136 (2018).
  36. J. Vučičević, N. Wentzell, M. Ferrero, and O. Parcollet, Practical consequences of the Luttinger-Ward functional multivaluedness for cluster DMFT methods, Phys. Rev. B 97, 125141 (2018).
  37. D. Springer, P. Chalupa, S. Ciuchi, G. Sangiovanni, and A. Toschi, Interplay between local response and vertex divergences in many-fermion systems with on-site attraction, Phys. Rev. B 101, 155148 (2020).
  38. M. Reitner, P. Chalupa, L. Del Re, D. Springer, S. Ciuchi, G. Sangiovanni, and A. Toschi, Attractive effect of a strong electronic repulsion: The physics of vertex divergences, Phys. Rev. Lett. 125, 196403 (2020).
  39. P. Chalupa, T. Schäfer, M. Reitner, D. Springer, S. Andergassen, and A. Toschi, Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems, Phys. Rev. Lett. 126, 056403 (2021).
  40. M. Pelz, S. Adler, M. Reitner, and A. Toschi, Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region, Phys. Rev. B 108, 155101 (2023).
  41. S. Adler, F. Krien, P. Chalupa-Gantner, G. Sangiovanni, and A. Toschi, Non-perturbative intertwining between spin and charge correlations: A “smoking gun” single-boson-exchange result, SciPost Phys. 16, 054 (2024).
  42. M. Reitner, L. Crippa, D. R. Fus, J. C. Budich, A. Toschi, and G. Sangiovanni, Protection of correlation-induced phase instabilities by exceptional susceptibilities, Phys. Rev. Res. 6, L022031 (2024).
  43. A. Kowalski, M. Reitner, L. Del Re, M. Chatzieleftheriou, A. Amaricci, A. Toschi, L. de’ Medici, G. Sangiovanni, and T. Schäfer, Thermodynamic stability at the two-particle level, Phys. Rev. Lett. 133, 066502 (2024).
  44. C. Watzenböck, M. Edelmann, D. Springer, G. Sangiovanni, and A. Toschi, Characteristic timescales of the local moment dynamics in Hund’s metals, Phys. Rev. Lett. 125, 086402 (2020).
  45. R. M. Wilcox, Bounds for the isothermal, adiabatic, and isolated static susceptibility tensors, Phys. Rev. 174, 624 (1968).
  46. F. Krien, E. G. C. P. van Loon, H. Hafermann, J. Otsuki, M. I. Katsnelson, and A. I. Lichtenstein, Conservation in two-particle self-consistent extensions of dynamical mean-field theory, Phys. Rev. B 96, 075155 (2017).
  47. F. Krien, E. G. C. P. van Loon, M. I. Katsnelson, A. I. Lichtenstein, and M. Capone, Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory, Phys. Rev. B 99, 245128 (2019).
  48. E. G. C. P. van Loon, H. Hafermann, A. I. Lichtenstein, and M. I. Katsnelson, Thermodynamic consistency of the charge response in dynamical mean-field based approaches, Phys. Rev. B 92, 085106 (2015).
  49. G. Kotliar, S. Murthy, and M. J. Rozenberg, Compressibility divergence and the finite temperature Mott transition, Phys. Rev. Lett. 89, 046401 (2002).
  50. P. Werner and A. J. Millis, Doping-driven Mott transition in the one-band Hubbard model, Phys. Rev. B 75, 085108 (2007).
  51. M. Eckstein, M. Kollar, M. Potthoff, and D. Vollhardt, Phase separation in the particle-hole asymmetric Hubbard model, Phys. Rev. B 75, 125103 (2007).
  52. R. Nourafkan, M. Côté, and A.-M. S. Tremblay, Charge fluctuations in lightly hole-doped cuprates: Effect of vertex corrections, Phys. Rev. B 99, 035161 (2019).
  53. E. G. C. P. van Loon, F. Krien, and A. A. Katanin, Bethe-salpeter equation at the critical end point of the Mott transition, Phys. Rev. Lett. 125, 136402 (2020).
  54. M. Reitner, Many-Electron Physics Beyond the Skeleton Series, Master’s thesis, TU Wien, 2025.
  55. P. Chalupa-Gantner, The Nonperturbative Feats of Local Electronic Correlation: The Physics of Irreducible Vertex Divergences, Ph.D. thesis, TU Wien, 2022.
  56. See Supplemental Material http://link.aps.org/supplemental/10.1103/ld8v-qpf8 for details on the two-particle formalism and the electron-phonon diagrammatics as well as supporting numerical data, which includes Refs. [57–64].
  57. E. Moghadas, Enhancement of Electron-Phonon Coupling Due to Nonperturbative Many-Electron Effects, Master’s thesis, TU Wien, 2023.
  58. E. Moghadas, M. Reitner, T. Wehling, G. Sangiovanni, S. Ciuchi, and A. Toschi, Dataset to “Effective enhancement of the electron-phonon coupling driven by nonperturbative electronic density fluctuations,” 10.48436/ccz0k-rg623 (2026).
  59. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics (Westview Press, Boulder, Colorado, 1992).
  60. T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism, Springer Series in Solid-State Sciences, (Springer, Berlin, 1985), Vol. 56.
  61. E. Pavarini, E. Koch, A. Lichtenstein, and D. Vollhardt, The LDA+DMFT Approach to Strongly Correlated Materials, Vol. 1 (Forschungszentrum, Jülich, 2011).
  62. A. Galler, P. Thunström, P. Gunacker, J. M. Tomczak, and K. Held, Ab initio dynamical vertex approximation, Phys. Rev. B 95, 115107 (2017).
  63. G. Baym and L. P. Kadanoff, Conservation laws and correlation functions, Phys. Rev. 124, 287 (1961).
  64. N. E. Bickers and S. R. White, Conserving approximations for strongly fluctuating electron systems. II. Numerical results and parquet extension, Phys. Rev. B 43, 8044 (1991).
  65. V. Janiš and V. Pokorný, Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems, Phys. Rev. B 90, 045143 (2014).
  66. O. Gunnarsson, T. Schäfer, J. P. F. LeBlanc, J. Merino, G. Sangiovanni, G. Rohringer, and A. Toschi, Parquet decomposition calculations of the electronic self-energy, Phys. Rev. B 93, 245102 (2016).
  67. P. Thunström, O. Gunnarsson, S. Ciuchi, and G. Rohringer, Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom, Phys. Rev. B 98, 235107 (2018).
  68. H. Eßl, M. Reitner, G. Sangiovanni, and A. Toschi, General Shiba mapping for on-site four-point correlation functions, Phys. Rev. Res. 6, 033061 (2024).
  69. E. Kozik, M. Ferrero, and A. Georges, Nonexistence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models, Phys. Rev. Lett. 114, 156402 (2015).
  70. H. Eßl, M. Reitner, E. Kozik, and A. Toschi, How to stay on the physical branch in self-consistent many-electron approaches, arXiv:2502.01420.
  71. T. B. Mazitov and A. A. Katanin, Local magnetic moment formation and Kondo screening in the half-filled single-band Hubbard model, Phys. Rev. B 105, L081111 (2022).
  72. T. B. Mazitov and A. A. Katanin, Effect of local magnetic moments on spectral properties and resistivity near interaction- and doping-induced Mott transitions, Phys. Rev. B 106, 205148 (2022).
  73. M. Wallerberger, A. Hausoel, P. Gunacker, A. Kowalski, N. Parragh, F. Goth, K. Held, and G. Sangiovanni, w2dynamics: Local one- and two-particle quantities from dynamical mean field theory, Comput. Phys. Commun. 235, 388 (2019).
  74. 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).
  75. It is important to emphasize here that different from, e.g., antiferromagnetic phase transitions, the phase-separation instability relevant for our study belongs to the Ising universality class. Hence, it will not necessarily be destroyed by spatial fluctuations beyond DMFT even in the 2D system considered.

  76. Rigorously speaking, one would expect the OZ momentum dependence of [χqc]−1 or ([γq]−1) to be corrected as |q|2−η, η=14 being the corresponding anomalous exponent of the 2D Ising class [77].

  77. K. Huang, Statistical Mechanics, 2nd ed. (John Wiley & Sons, New York, 1987).
  78. Note that even the explicit inclusion of the anomalous exponent η in the OZ expression would not prevent such a divergence, which would occur with a slightly modified scaling, ∼ξ32.

  79. This difference is due to the purely static nature of χq=0c(ω), which directly reflects the conservation of the total electric charge in the system.

  80. A more detailed discussion of the different class of el-ph diagrams and their scaling behavior in ξ, based on a rather general treatment à la ab initio DΓA [81], can be found in [56].

  81. A. Toschi, G. Rohringer, A. Katanin, and K. Held, Ab initio calculations with the dynamical vertex approximation, Ann. Phys. (Berlin) 523, 698 (2011).
  82. A. Rubtsov, M. Katsnelson, and A. Lichtenstein, Dual boson approach to collective excitations in correlated fermionic systems, Ann. Phys. (Amsterdam) 327, 1320 (2012).
  83. E. G. C. P. van Loon, A. I. Lichtenstein, M. I. Katsnelson, O. Parcollet, and H. Hafermann, Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model, Phys. Rev. B 90, 235135 (2014).
  84. M. Vandelli, J. Kaufmann, M. El-Nabulsi, V. Harkov, A. I. Lichtenstein, and E. A. Stepanov, Multi-band D-TRILEX approach to materials with strong electronic correlations, SciPost Phys. 13, 036 (2022).
  85. Z. P. Yin, A. Kutepov, and G. Kotliar, Correlation-enhanced electron-phonon coupling: Applications of GW and screened hybrid functional to bismuthates, chloronitrides, and other high-Tc superconductors, Phys. Rev. X 3, 021011 (2013).
  86. Z. Li, G. Antonius, M. Wu, F. H. da Jornada, and S. G. Louie, Electron-phonon coupling from ab initio linear-response theory within the GW method: Correlation-enhanced interactions and superconductivity in Ba1−xKxBiO3, Phys. Rev. Lett. 122, 186402 (2019).
  87. Z. Yuan, P. Zheng, Y. Peng, R. Liu, X. Ma, G. Wang, T. Yu, and Z. Yin, Correlation-enhanced electron-phonon coupling and superconductivity in (Ba,K)SbO3 superconductors, Phys. Rev. B 105, 014517 (2022).
  88. J. G. Bednorz and K. A. Muller, Possible high Tc superconductivity in the Ba-La-Cu-O system, Z. Phys. B 64, 189 (1986).
  89. P. W. Anderson, The resonating valence bond state in La2CuO4 and superconductivity, Science 235, 1196 (1987).
  90. F. C. Zhang and T. M. Rice, Effective hamiltonian for the superconducting Cu oxides, Phys. Rev. B 37, 3759 (1988).
  91. D. J. Scalapino, A common thread: The pairing interaction for unconventional superconductors, Rev. Mod. Phys. 84, 1383 (2012).
  92. D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity in an infinite-layer nickelate, Nature (London) 572, 624 (2019).
  93. M. Kitatani, L. Si, O. Janson, R. Arita, Z. Zhong, and K. Held, Nickelate superconductors—A renaissance of the one-band Hubbard model, npj Quantum Mater. 5, 59 (2020).
  94. M. Grilli, R. Raimondi, C. Castellani, C. Di Castro, and G. Kotliar, Phase separation and superconductivity in the U=∞ limit of the extended multiband Hubbard model, Int. J. Mod. Phys. B 05, 309 (1991).
  95. S. M. O’Mahony, W. Ren, W. Chen, Y. X. Chong, X. Liu, H. Eisaki, S. Uchida, M. H. Hamidian, and J. C. S. Davis, On the electron pairing mechanism of copper-oxide high temperature superconductivity, Proc. Natl. Acad. Sci. U.S.A. 119, e2207449119 (2022).
  96. B. Bacq-Labreuil, B. Lacasse, A.-M. S. Tremblay, D. Sénéchal, and K. Haule, Toward an ab initio theory of high-temperature superconductors: A study of multilayer cuprates, Phys. Rev. X 15, 021071 (2025).
  97. K. Haule and G. Kotliar, Coherence–incoherence crossover in the normal state of iron oxypnictides and importance of Hund’s rule coupling, New J. Phys. 11, 025021 (2009).
  98. L. de’ Medici, J. Mravlje, and A. Georges, Janus-faced influence of Hund’s rule coupling in strongly correlated materials, Phys. Rev. Lett. 107, 256401 (2011).
  99. S. Mandal, R. E. Cohen, and K. Haule, Strong pressure-dependent electron-phonon coupling in FeSe, Phys. Rev. B 89, 220502(R) (2014).
  100. L. de’ Medici, Hund’s induced fermi-liquid instabilities and enhanced quasiparticle interactions, Phys. Rev. Lett. 118, 167003 (2017).
  101. P. Villar Arribi and L. de’ Medici, Hund-enhanced electronic compressibility in FeSe and its correlation with Tc, Phys. Rev. Lett. 121, 197001 (2018).
  102. A. Isidori, M. Berović, L. Fanfarillo, L. de’ Medici, M. Fabrizio, and M. Capone, Charge disproportionation, mixed valence, and Janus effect in multiorbital systems: A tale of two insulators, Phys. Rev. Lett. 122, 186401 (2019).
  103. M. Chatzieleftheriou, A. Kowalski, M. Berović, A. Amaricci, M. Capone, L. De Leo, G. Sangiovanni, and L. de’ Medici, Mott quantum critical points at finite doping, Phys. Rev. Lett. 130, 066401 (2023).
  104. A. Georges, L. de’ Medici, and J. Mravlje, Strong correlations from Hund’s coupling, Annu. Rev. Condens. Matter Phys. 4, 137 (2013).
  105. E. Berger, P. Valášek, and W. von der Linden, Two-dimensional Hubbard-Holstein model, Phys. Rev. B 52, 4806 (1995).
  106. A. Macridin, B. Moritz, M. Jarrell, and T. Maier, Synergistic polaron formation in the Hubbard-Holstein model at small doping, Phys. Rev. Lett. 97, 056402 (2006).
  107. N. C. Costa, K. Seki, S. Yunoki, and S. Sorella, Phase diagram of the two-dimensional Hubbard-Holstein model, Commun. Phys. 3, 80 (2020).
  108. G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov, and K. Held, Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory, Rev. Mod. Phys. 90, 025003 (2018).
  109. L. Del Re and A. Toschi, Dynamical vertex approximation for many-electron systems with spontaneously broken SU(2) symmetry, Phys. Rev. B 104, 085120 (2021).
  110. G. Rohringer, A. Valli, and A. Toschi, Local electronic correlation at the two-particle level, Phys. Rev. B 86, 125114 (2012).
  111. G. Rohringer, New Routes Toward a Theoretical Treatment of Nonlocal Electronic Correlations, Ph.D. thesis, Technischen Universität Wien, 2014.
  112. M. Reitner, Dychotomy between Local and Uniform Compressibility in Correlated Systems: The Role of the Irreducible Vertex, Master’s thesis, TU Wien, 2020.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation