Papers
Topics
Authors
Recent
Search
2000 character limit reached

Mott transition and pseudogap of the square-lattice Hubbard model: results from center-focused cellular dynamical mean-field theory

Published 26 Oct 2023 in cond-mat.str-el | (2310.17302v2)

Abstract: The recently proposed center-focused post-processing procedure [Phys. Rev. Research 2, 033476 (2020)] of cellular dynamical mean-field theory suggests that central sites of large impurity clusters are closer to the exact solution of the Hubbard model than the edge sites. In this paper, we systematically investigate results in the spirit of this center-focused scheme for several cluster sizes up to $8\times 8$ in and out of particle-hole symmetry. First we analyze the metal-insulator crossovers and transitions of the half-filled Hubbard model on a simple square lattice. We find that the critical interaction of the crossover is reduced with increasing cluster sizes and the critical temperature abruptly drops for the $4\times 4$ cluster. Second, for this cluster size, we apply the center-focused scheme to a system with more realistic tight-binding parameters, investigating its pseudogap regime as a function of temperature and doping, where we find doping dependent metal-insulator crossovers, Lifshitz transitions and a strongly renormalized Fermi-liquid regime. Additionally to diagnosing the real space origin of the suppressed antinodal spectral weight in the pseudogap regime, we can infer hints towards underlying charge ordering tendencies.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (96)
  1. M. Imada, A. Fujimori and Y. Tokura, Metal-insulator transitions, Rev. Mod. Phys. 70, 1039 (1998), 10.1103/RevModPhys.70.1039.
  2. D. B. McWhan, T. M. Rice and J. P. Remeika, Mott transition in cr-doped v2subscriptnormal-v2{\mathrm{v}}_{2}roman_v start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPTo3subscriptnormal-o3{\mathrm{o}}_{3}roman_o start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT, Phys. Rev. Lett. 23, 1384 (1969), 10.1103/PhysRevLett.23.1384.
  3. Mott–Hubbard transition in V22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPTO33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT revisited, physica status solidi (b) 250, 1251 (2013), https://doi.org/10.1002/pssb.201248476, https://onlinelibrary.wiley.com/doi/pdf/10.1002/pssb.201248476.
  4. H. Alloul, T. Ohno and P. Mendels, Y89superscriptnormal-Y89{}^{89}\mathrm{Y}start_FLOATSUPERSCRIPT 89 end_FLOATSUPERSCRIPT roman_Y NMR evidence for a fermi-liquid behavior in YBa2subscriptnormal-YBa2{\mathrm{YBa}}_{2}roman_YBa start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPTCu3subscriptnormal-Cu3{\mathrm{Cu}}_{3}roman_Cu start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPTO6+xsubscriptnormal-O6normal-x{\mathrm{O}}_{6+\mathrm{x}}roman_O start_POSTSUBSCRIPT 6 + roman_x end_POSTSUBSCRIPT, Phys. Rev. Lett. 63, 1700 (1989), 10.1103/PhysRevLett.63.1700.
  5. Evolution of the pseudogap from Fermi arcs to the nodal liquid, Nature Physics 2, 447 (2006), 10.1038/nphys334, cond-mat/0605499.
  6. J. Hubbard, Electron Correlations in Narrow Energy Bands, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 276, 238 (1963), 10.1098/rspa.1963.0204.
  7. J. Hubbard and B. H. Flowers, Electron correlations in narrow energy bands iii. an improved solution, Proc. R. Soc. London, Sect. A 281, 401 (1964), 10.1098/rspa.1964.0190.
  8. M. C. Gutzwiller, Effect of Correlation on the Ferromagnetism of Transition Metals, Phys. Rev. Lett. 10, 159 (1963), 10.1103/PhysRevLett.10.159.
  9. J. Kanamori, Electron Correlation and Ferromagnetism of Transition Metals, Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275.
  10. The Hubbard Model, Annual Review of Condensed Matter Physics 13 (2022), 10.1146/annurev-conmatphys-031620-102024, https://doi.org/10.1146/annurev-conmatphys-031620-102024.
  11. The Hubbard Model: A Computational Perspective, Annual Review of Condensed Matter Physics 13 (2022), 10.1146/annurev-conmatphys-090921-033948, https://doi.org/10.1146/annurev-conmatphys-090921-033948.
  12. W. Metzner and D. Vollhardt, Correlated Lattice Fermions in d=∞𝑑d=\inftyitalic_d = ∞ Dimensions, Phys. Rev. Lett. 62, 324 (1989), 10.1103/PhysRevLett.62.324.
  13. A. Georges and G. Kotliar, Hubbard model in infinite dimensions, Phys. Rev. B 45, 6479 (1992), 10.1103/PhysRevB.45.6479.
  14. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13 (1996), 10.1103/RevModPhys.68.13.
  15. Quantum cluster theories, Rev. Mod. Phys. 77, 1027 (2005), 10.1103/RevModPhys.77.1027.
  16. Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory, Rev. Mod. Phys. 90, 025003 (2018), 10.1103/RevModPhys.90.025003.
  17. Antiferromagnetism and d-wave superconductivity in cuprates: A cluster dynamical mean-field theory, Phys. Rev. B 62, R9283 (2000), 10.1103/PhysRevB.62.R9283.
  18. Cellular Dynamical Mean Field Approach to Strongly Correlated Systems, Phys. Rev. Lett. 87, 186401 (2001), 10.1103/PhysRevLett.87.186401.
  19. A. Liebsch, H. Ishida and J. Merino, Multisite versus multiorbital Coulomb correlations studied within finite-temperature exact diagonalization dynamical mean-field theory, Phys. Rev. B 78, 165123 (2008), 10.1103/PhysRevB.78.165123.
  20. Cluster-size dependence in cellular dynamical mean-field theory, Phys. Rev. B 85, 035102 (2012), 10.1103/PhysRevB.85.035102.
  21. S. Moukouri and M. Jarrell, Absence of a Slater Transition in the Two-Dimensional Hubbard Model, Phys. Rev. Lett. 87, 167010 (2001), 10.1103/PhysRevLett.87.167010.
  22. E. Gull and A. J. Millis, Energetics of superconductivity in the two-dimensional Hubbard model, Phys. Rev. B 86, 241106 (2012), 10.1103/PhysRevB.86.241106.
  23. Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model, Phys. Rev. Lett. 110, 216405 (2013), 10.1103/PhysRevLett.110.216405.
  24. Mott transition, widom line, and pseudogap in the half-filled triangular lattice hubbard model, Phys. Rev. B 107, 125159 (2023), 10.1103/PhysRevB.107.125159.
  25. O. Parcollet, G. Biroli and G. Kotliar, Cluster Dynamical Mean Field Analysis of the Mott Transition, Phys. Rev. Lett. 92, 226402 (2004), 10.1103/PhysRevLett.92.226402.
  26. A cellular dynamical mean field theory approach to Mottness, Annals of Physics 321, 1682 (2006), https://doi.org/10.1016/j.aop.2006.03.009, July 2006 Special Issue.
  27. H. Park, K. Haule and G. Kotliar, Cluster dynamical mean field theory of the mott transition, Phys. Rev. Lett. 101, 186403 (2008), 10.1103/PhysRevLett.101.186403.
  28. Finite Doping Signatures of the Mott Transition in the Two-Dimensional Hubbard Model, Phys. Rev. Lett. 104, 226402 (2010), 10.1103/PhysRevLett.104.226402.
  29. Dynamical Breakup of the Fermi Surface in a Doped Mott Insulator, Phys. Rev. Lett. 95, 106402 (2005), 10.1103/PhysRevLett.95.106402.
  30. Pseudogap induced by short-range spin correlations in a doped Mott insulator, Phys. Rev. B 73, 165114 (2006), 10.1103/PhysRevB.73.165114.
  31. Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators, Phys. Rev. B 77, 184516 (2008), 10.1103/PhysRevB.77.184516.
  32. Strong Coupling Superconductivity, Pseudogap, and Mott Transition, Phys. Rev. Lett. 108, 216401 (2012), 10.1103/PhysRevLett.108.216401.
  33. Ergodicity of the hybridization-expansion monte carlo algorithm for broken-symmetry states, Phys. Rev. B 89, 165113 (2014), 10.1103/PhysRevB.89.165113.
  34. c𝑐citalic_c-axis resistivity, pseudogap, superconductivity, and Widom line in doped Mott insulators, Phys. Rev. B 87, 041101 (2013), 10.1103/PhysRevB.87.041101.
  35. Coexistence of superconductivity and antiferromagnetism in the Hubbard model for cuprates, Phys. Rev. B 99, 184510 (2019), 10.1103/PhysRevB.99.184510.
  36. Signatures of the Mott transition in the antiferromagnetic state of the two-dimensional Hubbard model, Phys. Rev. B 95, 235109 (2017), 10.1103/PhysRevB.95.235109.
  37. Effects of interaction strength, doping, and frustration on the antiferromagnetic phase of the two-dimensional Hubbard model, Phys. Rev. B 96, 241109 (2017), 10.1103/PhysRevB.96.241109.
  38. Real-space cluster dynamical mean-field theory: Center-focused extrapolation on the one- and two particle-levels, Phys. Rev. Research 2, 033476 (2020), 10.1103/PhysRevResearch.2.033476.
  39. A. N. Rubtsov, V. V. Savkin and A. I. Lichtenstein, Continuous-time quantum Monte Carlo method for fermions, Phys. Rev. B 72, 035122 (2005), 10.1103/PhysRevB.72.035122.
  40. Continuous-time Monte Carlo methods for quantum impurity models, Rev. Mod. Phys. 83, 349 (2011), 10.1103/RevModPhys.83.349.
  41. Triqs: A toolbox for research on interacting quantum systems, Computer Physics Communications 196, 398 (2015), https://doi.org/10.1016/j.cpc.2015.04.023.
  42. M. D. M. Meixner, On the Phase Diagram of the Hubbard-Model in Real-Space Extensions of Dynamical Mean-Field Theory, Master’s thesis, University of Tübingen (2021).
  43. R. N. Silver, D. S. Sivia and J. E. Gubernatis, Maximum-entropy method for analytic continuation of quantum Monte Carlo data, Phys. Rev. B 41, 2380 (1990), 10.1103/PhysRevB.41.2380.
  44. Maximum entropy formalism for the analytic continuation of matrix-valued Green’s functions, Phys. Rev. B 96, 155128 (2017), 10.1103/PhysRevB.96.155128.
  45. R. Bryan, Maximum entropy analysis of oversampled data problems, Eur Biophys J 18, 165 (1990), https://doi.org/10.1007/BF02427376.
  46. Extended Crossover from a Fermi Liquid to a Quasiantiferromagnet in the Half-Filled 2D Hubbard Model, Phys. Rev. Lett. 124, 017003 (2020), 10.1103/PhysRevLett.124.017003.
  47. Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model, Phys. Rev. X 11, 011058 (2021), 10.1103/PhysRevX.11.011058.
  48. M. Pelz, Investigation of the highly non-perturbative nature of the Mott-Hubbard metal insulator transition: Vertex divergences in the coexistence region, Master’s thesis, TU Wien (2022).
  49. Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region, Phys. Rev. B 108, 155101 (2023), 10.1103/PhysRevB.108.155101.
  50. Fate of the false Mott-Hubbard transition in two dimensions, Phys. Rev. B 91, 125109 (2015), 10.1103/PhysRevB.91.125109.
  51. N. Blümer, Mott-Hubbard Metal-Insulator Transition and Optical Conductivity in High Dimensions, Ph.D. thesis, University of Augsburg (2002).
  52. D. Vollhardt, Dynamical mean-field theory for correlated electrons, Annalen der Physik 524, 1 (2012), https://doi.org/10.1002/andp.201100250.
  53. T. Schäfer, Classical and quantum phase transitions in strongly correlated electron systems, Ph.D. thesis, Vienna University of Technology, https://doi.org/10.34726/hss.2016.28659 (2016).
  54. Mott transition and high-temperature crossovers at half-filling, https://doi.org/10.48550/arXiv.2004.02302 (2020), 2004.02302.
  55. N. D. Mermin and H. Wagner, Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models, Phys. Rev. Lett. 17, 1307 (1966), 10.1103/PhysRevLett.17.1307.
  56. T. Schäfer, A. Toschi and K. Held, Dynamical vertex approximation for the two-dimensional Hubbard model, Journal of Magnetism and Magnetic Materials 400, 107 (2016), https://doi.org/10.1016/j.jmmm.2015.07.103, Proceedings of the 20th International Conference on Magnetism (Barcelona) 5-10 July 2015.
  57. Non-Perturbative Many-Body Approach to the Hubbard Model and Single-Particle Pseudogap, J. Phys. I France 7, 1309 (1997), 10.1051/jp1:1997135.
  58. K. Borejsza and N. Dupuis, Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: A nonlinear sigma model approach, Phys. Rev. B 69 (2004), 10.1103/physrevb.69.085119.
  59. Y. M. Vilk, Criteria and analytical results for the pseudogap at the Van Hove point in two dimensions, Phys. Rev. B 108, 235110 (2023), 10.1103/PhysRevB.108.235110.
  60. Local and nonlocal electronic correlations at the metal-insulator transition in the Hubbard model in two dimensions, arXiv (2023), https://doi.org/10.48550/arXiv.2312.03123, 2312.03123.
  61. Mott Insulating States with Competing Orders in the Triangular Lattice Hubbard Model, Phys. Rev. X 11, 041013 (2021), 10.1103/PhysRevX.11.041013.
  62. J. M. Luttinger, Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions, Phys. Rev. 119, 1153 (1960), 10.1103/PhysRev.119.1153.
  63. I. Dzyaloshinskii, Some consequences of the Luttinger theorem: The Luttinger surfaces in non-Fermi liquids and Mott insulators, Phys. Rev. B 68, 085113 (2003), 10.1103/PhysRevB.68.085113.
  64. J. Skolimowski and M. Fabrizio, Luttinger’s theorem in the presence of Luttinger surfaces, Phys. Rev. B 106, 045109 (2022), 10.1103/PhysRevB.106.045109.
  65. Emergent Properties of the Periodic Anderson Model: a High-Resolution, Real-Frequency Study of Heavy-Fermion Quantum Criticality, https://doi.org/10.48550/arXiv.2310.12672 (2023), 2310.12672.
  66. Hubbard Model Physics in Transition Metal Dichalcogenide Moiré Bands, Phys. Rev. Lett. 121, 026402 (2018), 10.1103/PhysRevLett.121.026402.
  67. First-Matsubara-frequency rule in a Fermi liquid. I. Fermionic self-energy, Phys. Rev. B 86, 155136 (2012), 10.1103/PhysRevB.86.155136.
  68. Origin and fate of the pseudogap in the doped Hubbard model, 10.48550/arxiv.2209.09237 (2022).
  69. One-band tight-binding model parametrization of the high-Tcsubscript𝑇𝑐{T}_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT cuprates including the effect of kzsubscript𝑘𝑧{k}_{z}italic_k start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT dispersion, Phys. Rev. B 72, 054519 (2005), 10.1103/PhysRevB.72.054519.
  70. Nickelate superconductors—a renaissance of the one-band Hubbard model, npj Quantum Materials 5 (2020), 10.1038/s41535-020-00260-y.
  71. Magnetic correlations in infinite-layer nickelates: An experimental and theoretical multimethod study, Phys. Rev. Research 4, 023093 (2022), 10.1103/PhysRevResearch.4.023093.
  72. M. Klett, P. Hansmann and T. Schäfer, Magnetic Properties and Pseudogap Formation in Infinite-Layer Nickelates: Insights From the Single-Band Hubbard Model, Frontiers in Physics 10 (2022), 10.3389/fphy.2022.834682.
  73. Pseudogap and Fermi-Surface Topology in the Two-Dimensional Hubbard Model, Proceedings of the National Academy of Sciences 115, E3665 (2018), 10.1073/pnas.1720580115.
  74. P. M. Bonetti and W. Metzner, SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model, Phys. Rev. B 106, 205152 (2022), 10.1103/PhysRevB.106.205152.
  75. P. M. Bonetti, Dissertation: Long-range order, bosonic fluctuations, and pseudogap in strongly correlated electron systems, 10.18419/OPUS-12480 (2022).
  76. Charge carrier drop at the onset of pseudogap behavior in the two-dimensional Hubbard model, Phys. Rev. B 101, 165142 (2020), 10.1103/PhysRevB.101.165142.
  77. Explaining the pseudogap through damping and antidamping on the Fermi surface by imaginary spin scattering, Communications Physics 5, 336 (2022), 10.1038/s42005-022-01117-5.
  78. Pseudogap and Fermi-Surface Topology in the Two-Dimensional Hubbard Model, Phys. Rev. X 8, 021048 (2018), 10.1103/PhysRevX.8.021048.
  79. J. Merino and O. Gunnarsson, Pseudogap and singlet formation in organic and cuprate superconductors, Phys. Rev. B 89, 245130 (2014), 10.1103/PhysRevB.89.245130.
  80. Fluctuation Diagnostics of the Electron Self-Energy: Origin of the Pseudogap Physics, Phys. Rev. Lett. 114, 236402 (2015), 10.1103/PhysRevLett.114.236402.
  81. T. Schäfer and A. Toschi, How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems, Journal of Physics: Condensed Matter 33, 214001 (2021), 10.1088/1361-648x/abeb44.
  82. Controlling Feynman diagrammatic expansions: Physical nature of the pseudogap in the two-dimensional Hubbard model, Phys. Rev. B 96, 041105 (2017), 10.1103/PhysRevB.96.041105.
  83. Stripes and spin-density waves in the doped two-dimensional Hubbard model: Ground state phase diagram, Phys. Rev. Research 4 (2022), 10.1103/physrevresearch.4.013239.
  84. S. Sorella, The phase diagram of the Hubbard model by Variational Auxiliary Field quantum Monte Carlo, https://doi.org/10.48550/arXiv.2101.07045 (2022), 2101.07045.
  85. Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model, Phys. Rev. X 13, 011007 (2023), 10.1103/PhysRevX.13.011007.
  86. Intertwined spin, charge, and pair correlations in thetwo-dimensional Hubbard model in thethermodynamic limit, Proceedings of the National Academy of Sciences 119, 7 (2022), https://doi.org/10.1073/pnas.2112806119.
  87. Stripe order from the perspective of the Hubbard model, npj Quantum Materials 3, 22 (2018), 10.1038/s41535-018-0097-0.
  88. Fermi arcs from dynamical variational Monte Carlo, Phys. Rev. B 106, 245132 (2022), 10.1103/PhysRevB.106.245132.
  89. N. Enenkel, M. Garst and P. Schmitteckert, Applicability and limitations of cluster perturbation theory for Hubbard models, https://doi.org/10.1140/epjs/s11734-023-00976-5 (2023).
  90. Functional renormalization group approach to correlated fermion systems, Rev. Mod. Phys. 84, 299 (2012), 10.1103/RevModPhys.84.299.
  91. The nonperturbative functional renormalization group and its applications, Physics Reports 910, 1 (2021), 10.1016/j.physrep.2021.01.001.
  92. Interaction-Induced Adiabatic Cooling and Antiferromagnetism of Cold Fermions in Optical Lattices, Phys. Rev. Lett. 95, 056401 (2005), 10.1103/PhysRevLett.95.056401.
  93. Interaction-induced adiabatic cooling for antiferromagnetism in optical lattices, Phys. Rev. B 76, 064402 (2007), 10.1103/PhysRevB.76.064402.
  94. A. A. Katanin, Fulfillment of Ward identities in the functional renormalization group approach, Phys. Rev. B 70, 115109 (2004), 10.1103/PhysRevB.70.115109.
  95. C. Hille, The role of the self-energy in the functional renormalization group description of interacting Fermi systems, Ph.D. thesis, Universität Tübingen (2020).
  96. S.-S. B. Lee, J. von Delft and A. Weichselbaum, Doublon-Holon Origin of the Subpeaks at the Hubbard Band Edges, Phys. Rev. Lett. 119, 236402 (2017), 10.1103/PhysRevLett.119.236402.
Citations (4)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up