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  • Letter
  • Open Access

Time-dependent ghost Gutzwiller nonequilibrium dynamics

Daniele Guerci1, Massimo Capone2,3, and Nicola Lanatà4,1,*

  • 1Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
  • 2Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
  • 3CNR-IOM, Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, Via Bonomea 265, 34136 Trieste, Italy
  • 4School of Physics and Astronomy, Rochester Institute of Technology, 84 Lomb Memorial Drive, Rochester, New York 14623, USA

  • *Corresponding author: nxlsps@rit.edu
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Phys. Rev. Research 5, L032023 – Published 17 August, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032023

Abstract

We introduce the time-dependent ghost Gutzwiller approximation (TD-gGA), a nonequilibrium extension of the ghost Gutzwiller approximation (gGA), a powerful variational approach which systematically improves on the standard Gutzwiller method by including auxiliary degrees of freedom. We demonstrate the effectiveness of TD-gGA by studying the quench dynamics of the single-band Hubbard model as a function of the number of auxiliary parameters. Our results show that TD-gGA captures the relaxation of local observables, in contrast with the time-dependent Gutzwiller method. This systematic and qualitative improvement leads to an accuracy comparable with time-dependent dynamical mean-field theory which comes at a much lower computational cost. These findings suggest that TD-gGA has the potential to enable extensive and accurate theoretical investigations of multiorbital correlated electron systems in nonequilibrium situations, with potential applications in the field of quantum control, Mott solar cells, and other areas where an accurate account of the nonequilibrium properties of strongly interacting quantum systems is required.

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References (62)

  1. A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011).
  2. A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, Femtosecond Structural Dynamics in VO2 During an Ultrafast Solid-Solid Phase Transition, Phys. Rev. Lett. 87, 237401 (2001).
  3. C. Giannetti, M. Capone, D. Fausti, M. Fabrizio, F. Parmigiani, and D. Mihailovic, Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach, Adv. Phys. 65, 58 (2016).
  4. A. de la Torre, D. M. Kennes, M. Claassen, S. Gerber, J. W. McIver, and M. A. Sentef, Colloquium: Nonthermal pathways to ultrafast control in quantum materials, Rev. Mod. Phys. 93, 041002 (2021).
  5. D. Jaksch, V. Venturi, J. I. Cirac, C. J. Williams, and P. Zoller, Creation of a Molecular Condensate by Dynamically Melting a Mott Insulator, Phys. Rev. Lett. 89, 040402 (2002).
  6. D. Jaksch and P. Zoller, The cold atom Hubbard toolbox, Ann. Phys. 315, 52 (2005).
  7. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  8. T. Esslinger, Fermi-Hubbard physics with atoms in an optical lattice, Annu. Rev. Condens. Matter Phys. 1, 129 (2010).
  9. I. Bloch, J. Dalibard, and S. Nascimbène, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012).
  10. A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, A cold-atom Fermi–Hubbard antiferromagnet, Nature (London) 545, 462 (2017).
  11. J. H. Drewes, L. A. Miller, E. Cocchi, C. F. Chan, N. Wurz, M. Gall, D. Pertot, F. Brennecke, and M. Köhl, Antiferromagnetic Correlations in Two-Dimensional Fermionic Mott-Insulating and Metallic Phases, Phys. Rev. Lett. 118, 170401 (2017).
  12. M. Yan, H.-Y. Hui, M. Rigol, and V. W. Scarola, Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder, Phys. Rev. Lett. 119, 073002 (2017).
  13. M. Yan, H.-Y. Hui, and V. W. Scarola, Dynamics of disordered states in the Bose-Hubbard model with confinement, Phys. Rev. A 95, 053624 (2017).
  14. E. Manousakis, Photovoltaic effect for narrow-gap Mott insulators, Phys. Rev. B 82, 125109 (2010).
  15. P. Werner, K. Held, and M. Eckstein, Role of impact ionization in the thermalization of photoexcited Mott insulators, Phys. Rev. B 90, 235102 (2014).
  16. L. Wang, Y. Li, A. Bera, C. Ma, F. Jin, K. Yuan, W. Yin, A. David, W. Chen, W. Wu, W. Prellier, S. Wei, and T. Wu, Device Performance of the Mott Insulator LaVO3 as a Photovoltaic Material, Phys. Rev. Appl. 3, 064015 (2015).
  17. F. Petocchi, S. Beck, C. Ederer, and P. Werner, Hund excitations and the efficiency of Mott solar cells, Phys. Rev. B 100, 075147 (2019).
  18. F. Petocchi, J. Chen, J. Li, M. Eckstein, and P. Werner, Photoinduced charge dynamics in 1T−TaS2, Phys. Rev. B 107, 165102 (2023).
  19. 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).
  20. M. Eckstein, M. Kollar, and P. Werner, Thermalization after an Interaction Quench in the Hubbard Model, Phys. Rev. Lett. 103, 056403 (2009).
  21. M. Eckstein, M. Kollar, and P. Werner, Interaction quench in the Hubbard model: Relaxation of the spectral function and the optical conductivity, Phys. Rev. B 81, 115131 (2010).
  22. 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).
  23. N. Lanatà, T.-H. Lee, Y.-X. Yao, and V. Dobrosavljević, Emergent Bloch excitations in Mott matter, Phys. Rev. B 96, 195126 (2017).
  24. 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).
  25. D. Guerci, M. Capone, and M. Fabrizio, Exciton Mott transition revisited, Phys. Rev. Mater. 3, 054605 (2019).
  26. M. C. Gutzwiller, Correlation of electrons in a narrow s band, Phys. Rev. 137, A1726 (1965).
  27. N. Lanatà, Y. 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).
  28. J. R. Moreno, G. Carleo, A. Georges, and J. Stokes, Fermionic wave functions from neural-network constrained hidden states, Proc. Natl. Acad. Sci. USA 119, e2122059119 (2022).
  29. N. Lanatà, Operatorial formulation of the ghost rotationally invariant slave-boson theory, Phys. Rev. B 105, 045111 (2022).
  30. 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).
  31. G. Kotliar and A. E. Ruckenstein, New Functional Integral Approach to Strongly Correlated Fermi Systems: The Gutzwiller Approximation as a Saddle Point, Phys. Rev. Lett. 57, 1362 (1986).
  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.-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).
  34. 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).
  35. 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, arXiv:2305.11128.
  36. M. Fabrizio, The out-of-equilibrium time-dependent Gutzwiller approximation, in New Materials for Thermoelectric Applications: Theory and Experiment, edited by V. Zlatic and A. Hewson, NATO Science for Peace and Security Series B: Physics and Biophysics (Springer, Dordrecht, 2013), pp. 247–273.
  37. M. Schiró and M. Fabrizio, Time-Dependent Mean Field Theory for Quench Dynamics in Correlated Electron Systems, Phys. Rev. Lett. 105, 076401 (2010).
  38. N. Lanatà and H. U. R. Strand, Time-dependent and steady-state Gutzwiller approach for nonequilibrium transport in nanostructures, Phys. Rev. B 86, 115310 (2012).
  39. G. Seibold and J. Lorenzana, Time-Dependent Gutzwiller Approximation for the Hubbard Model, Phys. Rev. Lett. 86, 2605 (2001).
  40. E. v. Oelsen, G. Seibold, and J. Bünemann, Time-Dependent Gutzwiller Theory for Multiband Hubbard Models, Phys. Rev. Lett. 107, 076402 (2011).
  41. M. Schiró, Nonequilibrium dynamics across an impurity quantum critical point due to quantum quenches, Phys. Rev. B 86, 161101(R) (2012).
  42. M. Sandri, M. Schiró, and M. Fabrizio, Linear ramps of interaction in the fermionic Hubbard model, Phys. Rev. B 86, 075122 (2012).
  43. M. Sandri and M. Fabrizio, Nonequilibrium dynamics in the antiferromagnetic Hubbard model, Phys. Rev. B 88, 165113 (2013).
  44. M. M. Wysokiński and M. Fabrizio, Interplay of charge and spin dynamics after an interaction quench in the Hubbard model, Phys. Rev. B 96, 201115(R) (2017).
  45. G. Mazza, From sudden quench to adiabatic dynamics in the attractive Hubbard model, Phys. Rev. B 96, 205110 (2017).
  46. D. Guerci, Transport through a magnetic impurity: A slave-spin approach, Phys. Rev. B 99, 195409 (2019).
  47. R. Jördens, N. Strohmaier, K. Günter, H. Moritz, and T. Esslinger, A Mott insulator of fermionic atoms in an optical lattice, Nature (London) 455, 204 (2008).
  48. U. Schneider, L. Hackermüller, J. P. Ronzheimer, S. Will, S. Braun, T. Best, I. Bloch, E. Demler, S. Mandt, D. Rasch et al., Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms, Nat. Phys. 8, 213 (2012).
  49. F. Schäfer, T. Fukuhara, S. Sugawa, Y. Takasu, and Y. Takahashi, Tools for quantum simulation with ultracold atoms in optical lattices, Nat. Rev. Phys. 2, 411 (2020).
  50. M. Moeckel and S. Kehrein, Interaction Quench in the Hubbard Model, Phys. Rev. Lett. 100, 175702 (2008).
  51. F. Goth and F. F. Assaad, Time and spatially resolved quench of the fermionic Hubbard model showing restricted equilibration, Phys. Rev. B 85, 085129 (2012).
  52. F. K. Wilhelm, S. Kirchhoff, S. Machnes, N. Wittler, and D. Sugny, An introduction into optimal control for quantum technologies, arXiv:2003.10132.
  53. D. Guerci, Beyond simple variational approach for strongly correlated electron systems, Ph.D. thesis, Scuola Internazionale Superiore di Studi Avanzati, 2019, https://hdl.handle.net/20.500.11767/103994.
  54. R. Brankin, I. Gladwell, and L. Shampine, RKSUITE: A suite of explicit Runge-Kutta codes, in Contributions in Numerical Mathematics (World Scientific, Singapore, 1993), pp. 41–53.
  55. Our calculations have been performed setting the initial state at a very small interaction strength Ui=0.05. This is because the gGA variational landscape is degenerate in the limiting case U=0∀B≥3 and, therefore, the self-consistency procedure becomes numerically unstable.
  56. M. Schiró and M. Fabrizio, Quantum quenches in the Hubbard model: Time-dependent mean-field theory and the role of quantum fluctuations, Phys. Rev. B 83, 165105 (2011).
  57. F. A. Wolf, I. P. McCulloch, and U. Schollwöck, Solving nonequilibrium dynamical mean-field theory using matrix product states, Phys. Rev. B 90, 235131 (2014).
  58. D. Bauernfeind, X. Cao, E. M. Stoudenmire, and O. Parcollet, Minimally entangled typical thermal state algorithms for finite temperature Matsubara Green functions, Phys. Rev. B 105, 195107 (2022).
  59. J. Prior, A. W. Chin, S. F. Huelga, and M. B. Plenio, Efficient Simulation of Strong System-Environment Interactions, Phys. Rev. Lett. 105, 050404 (2010).
  60. L. Kohn and G. E. Santoro, Quenching the anderson impurity model at finite temperature: Entanglement and bath dynamics using matrix product states, arXiv:2107.02807.
  61. J. Thoenniss, M. Sonner, A. Lerose, and D. A. Abanin, Efficient method for quantum impurity problems out of equilibrium, Phys. Rev. B 107, L201115 (2023).
  62. N. Ng, G. Park, A. J. Millis, G. K.-L. Chan, and D. R. Reichman, Real-time evolution of Anderson impurity models via tensor network influence functionals, Phys. Rev. B 107, 125103 (2023).

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Phys. Rev. Research 5, L032023– Published 17 August, 2023
  • Received 24 March 2023
  • Revised 29 June 2023
  • Accepted 10 July 2023
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