Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
143 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Schwinger-Keldysh nonperturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models (2405.00765v4)

Published 1 May 2024 in quant-ph, cond-mat.str-el, hep-th, math-ph, and math.MP

Abstract: Open quantum systems with many interacting degrees of freedom pose a formidable challenge for presently available theoretical methods, especially when dissipative environment imposes non-Markovian dynamics on them with memory effects and revival of genuine quantum properties. Even the archetypical spin-boson model, where a single spin-1/2 interacts with an infinite bosonic bath, requires switching between methods for different choice of system and bath parameters. Here, we construct a field-theoretic framework as a single methodology that can handle many mutually interacting quantum spins of arbitrary value S, spatial dimensionality, system-bath coupling, bath temperature and spectral properties of the bath. Our framework combines Schwinger-Keldysh field theory (SKFT) with two-particle irreducible (2PI) action resumming a class of Feynman diagrams to an infinite order originating from 1/N expansion, where N is the number of Schwinger bosons to which the spin is mapped. Remarkably, the SKFT+2PI approach closely tracks numerically exact benchmarks for spin-boson in the non-Markovian regime obtained from hierarchical equations of motion or tensor network methods. Furthermore, we demonstrate the ability of our SKFT+2PI framework to compute two-spin correlators of an antiferromagnetic quantum spin chain whose edge spins are coupled to a set of three bosonic baths (one for each spin component) at different temperatures. The favorable numerical cost of solving integro-differential equations produced by SKFT+2PI framework with increasing number of spins, time steps or spatial dimensionality makes it a promising route for simulation of driven-dissipative systems in quantum computing or quantum magnonics and quantum spintronics in the presence of a single or multiple dissipative environments.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (69)
  1. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2007).
  2. I. de Vega and D. Alonso, Dynamics of non-Markovian open quantum systems, Rev. Mod. Phys. 89, 015001 (2017).
  3. G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  4. I. de Vega and M.-C. Bañuls, Thermofield-based chain-mapping approach for open quantum systems, Phys. Rev. A 92, 052116 (2015).
  5. F. Nathan and M. S. Rudner, Universal Lindblad equation for open quantum systems, Phys. Rev. B 102, 115109 (2020).
  6. T. Prosen, Third quantization: a general method to solve master equations for quadratic open Fermi systems, New Journal of Physics 10, 043026 (2008).
  7. L. E. Ballentine, Quantum Mechanics: A Modern Development (World Scientific, Singapore, 2014).
  8. L. M. Sieberer, M. Buchhold, and S. Diehl, Keldysh field theory for driven open quantum systems, Rep. Prog. Phys. 79, 096001 (2016).
  9. A. Kamenev, Field Theory of Non-Equilibrium Systems (Cambridge University Press, Cambridge, 2023).
  10. J. Berges, Nonequilibrium quantum fields: From cold atoms to cosmology, arXiv:1503.02907  (2015).
  11. E. A. Calzetta and B.-L. B. Hu, Nonequilibrium Quantum Field Theory (Cambridge University Press, Cambridge, 2008).
  12. F. Gelis, Quantum Field Theory: From Basics to Modern Topics (Cambridge University Press, Cambridge, 2019).
  13. F. Thompson and A. Kamenev, Field theory of many-body Lindbladian dynamics, Ann. Phys. 455, 169385 (2023).
  14. M. F. Maghrebi and A. V. Gorshkov, Nonequilibrium many-body steady states via Keldysh formalism, Phys. Rev. B 93, 014307 (2016).
  15. B. Gulácsi and G. Burkard, Signatures of non-Markovianity of a superconducting qubit, Phys. Rev. B 107, 174511 (2023).
  16. M. Babadi, E. Demler, and M. Knap, Far-from-equilibrium field theory of many-body quantum spin systems: Prethermalization and relaxation of spin spiral states in three dimensions, Phys. Rev. X 5, 041005 (2015).
  17. A. Schuckert, A. Orioli, and J. Berges, Nonequilibrium quantum spin dynamics from two-particle irreducible functional integral techniques in the Schwinger boson representation, Phys. Rev. B 98, 224304 (2018).
  18. M. Brown and I. Whittingham, Two-particle irreducible effective actions versus resummation: Analytic properties and self-consistency, Nucl. Phys. B 900, 477 (2015).
  19. H. Mera, T. G. Pedersen, and B. K. Nikolić, Hypergeometric resummation of self-consistent sunset diagrams for steady-state electron-boson quantum many-body systems out of equilibrium, Phys. Rev. B 94, 165429 (2016).
  20. H. Mera, T. G. Pedersen, and B. K. Nikolić, Fast summation of divergent series and resurgent transseries from Meijer-g𝑔gitalic_g approximants, Phys. Rev. D 97, 105027 (2018).
  21. J. M. Cornwall, R. Jackiw, and E. Tomboulis, Effective action for composite operators, Phys. Rev. D 10, 2428 (1974).
  22. N. Makri, Numerical path integral techniques for long time dynamics of quantum dissipative systems, J. Math. Phys. 36, 2430 (1995).
  23. H. Wang and M. Thoss, From coherent motion to localization: dynamics of the spin-boson model at zero temperature, New J. Phys. 10, 115005 (2008).
  24. H. Wang and M. Thoss, From coherent motion to localization: II. dynamics of the spin-boson model with sub-Ohmic spectral density at zero temperature, Chem. Phys. 370, 78 (2010).
  25. A. Strathearn, B. W. Lovett, and P. Kirton, Efficient real-time path integrals for non-Markovian spin-boson models, New J. Phys. 19, 093009 (2017).
  26. E. Ye and G. K.-L. Chan, Constructing tensor network influence functionals for general quantum dynamics, J. Chem. Phys. 155, 044104 (2021).
  27. M. Xu and J. Ankerhold, About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach, Eur. Phys. J. Spec. Top. 232, 3209–3217 (2023).
  28. M. Weber, Quantum Monte Carlo simulation of spin-boson models using wormhole updates, Phys. Rev. B 105, 165129 (2022).
  29. I. Vilkoviskiy and D. A. Abanin, A bound on approximating non-Markovian dynamics by tensor networks in the time domain, arXiv:2307.15592  (2023).
  30. Y. Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM), J. Chem. Phys. 153, 020901 (2020).
  31. G. Clos and H.-P. Breuer, Quantification of memory effects in the spin-boson model, Phys. Rev. A 86, 012115 (2012).
  32. S. Wenderoth, H.-P. Breuer, and M. Thoss, Non-Markovian effects in the spin-boson model at zero temperature, Phys. Rev. A 104, 012213 (2021).
  33. R. Bulla, N.-H. Tong, and M. Vojta, Numerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model, Phys. Rev. Lett. 91, 170601 (2003).
  34. F. B. Anders and A. Schiller, Spin precession and real-time dynamics in the Kondo model: Time-dependent numerical renormalization-group study, Phys. Rev. B 74, 245113 (2006).
  35. F. B. Anders, R. Bulla, and M. Vojta, Equilibrium and nonequilibrium dynamics of the sub-Ohmic spin-boson model, Phys. Rev. Lett. 98, 210402 (2007).
  36. M. Vojta, Numerical renormalization group for the sub-Ohmic spin-boson model: A conspiracy of errors, Phys. Rev. B 85, 115113 (2012).
  37. P. P. Orth, A. Imambekov, and K. Le Hur, Nonperturbative stochastic method for driven spin-boson model, Phys. Rev. B 87, 014305 (2013).
  38. F. Shibata and T. Arimitsu, Expansion formulas in nonequilibrium statistical mechanics, J. Phys. Soc. Japan 49, 891 (1980).
  39. Y. Tanimura and P. G. Wolynes, Quantum and classical Fokker-Planck equations for a Gaussian-Markovian noise bath, Phys. Rev. A 43, 4131 (1991).
  40. A. Lerose, M. Sonner, and D. A. Abanin, Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality, Phys. Rev. B 107, L060305 (2023).
  41. M. M. Rams and M. Zwolak, Breaking the entanglement barrier: Tensor network simulation of quantum transport, Phys. Rev. Lett. 124, 137701 (2020).
  42. F. García-Gaitán and B. K. Nikolić, Fate of entanglement in magnetism under Lindbladian or non-Markovian dynamics and conditions for their transition to Landau-Lifshitz-Gilbert classical dynamics, arXiv:2303.17596  (2023).
  43. R. Trivedi and J. I. Cirac, Transitions in computational complexity of continuous-time local open quantum dynamics, Phys. Rev. Lett. 129, 260405 (2022).
  44. U. Bajpai, A. Suresh, and B. K. Nikolić, Quantum many-body states and Green's functions of nonequilibrium electron-magnon systems: Localized spin operators versus their mapping to Holstein-Primakoff bosons, Phys. Rev. B 104, 184425 (2021).
  45. A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer, New York, 1994).
  46. A. Altland and B. Simons, Condensed Matter Field Theory (Cambridge University Press, Cambridge, 2023).
  47. J. Anders, C. R. J. Sait, and S. A. R. Horsley, Quantum Brownian motion for magnets, New J. Phys. 24, 033020 (2022).
  48. U. Bajpai and B. Nikolić, Time-retarded damping and magnetic inertia in the Landau-Lifshitz-Gilbert equation self-consistently coupled to electronic time-dependent nonequilibrium Green functions, Phys. Rev. B 99, 134409 (2019).
  49. S. Nakajima, On quantum theory of transport phenomena: Steady diffusion, Prog. Theor. Phys. 20, 948 (1958).
  50. R. Zwanzig, Ensemble method in the theory of irreversibility, J. Chem. Phys. 33, 1338 (1960).
  51. J. Rammer, Quantum Field Theory of Non-equilibrium States (Cambridge University Press, Cambridge, 2007).
  52. J. Berges, Controlled nonperturbative dynamics of quantum fields out of equilibrium, Nucl. Phys. A 699, 847 (2002).
  53. G. Aarts and J. Berges, Classical aspects of quantum fields far from equilibrium, Phys. Rev. Lett. 88, 041603 (2002).
  54. M. Kronenwett and T. Gasenzer, Far-from-equilibrium dynamics of an ultracold Fermi gas, Appl. Phys. B 102, 469 (2011).
  55. S. Borsányi, Nonequilibrium field theory from the 2PI effective action, arXiv: 0512308  (2005).
  56. G. Stefanucci and R. van Leeuwen, Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction (Cambridge University Press, Cambridge, 2013).
  57. L. Kantorovich, Generalized Langreth rules, Phys. Rev. B 101, 165408 (2020).
  58. G. Vidal, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett. 91, 147902 (2003).
  59. Y. Takahashi and H. Umezawa, Thermo field dynamics, Int. J. Mod. Phys. B 10, 1755 (1996).
  60. W. Gautschi, Orthogonal polynomials (in Matlab), J. Comput. Appl. Math. 178, 215 (2005).
  61. M. P. Woods and M. B. Plenio, Dynamical error bounds for continuum discretisation via Gauss quadrature rules–A Lieb-Robinson bound approach, J. Math. Phys. 57, 022105 (2016).
  62. C. Lubich, I. V. Oseledets, and B. Vandereycken, Time integration of tensor trains, SIAM J. Numer. Anal. 53, 917 (2015).
  63. C. Meier and D. Tannor, Non-Markovian evolution of the density operator in the presence of strong laser fields, J. Chem. Phys. 111, 3365 (1999).
  64. J. Johansson, P. Nation, and F. Nori, QuTiP: An open-source Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
  65. J. Johansson, P. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 184, 1234 (2013).
  66. A. Branschädel and T. Gasenzer, 2PI nonequilibrium versus transport equations for an ultracold Bose gas, J. Phys. B: At. Mol. Opt. Phys. 41, 135302 (2008).
  67. J. Lang, M. Buchhold, and S. Diehl, Field theory for the dynamics of the open O⁢(N)𝑂𝑁O(N)italic_O ( italic_N ) model, Phys. Rev. B 109, 064310 (2024).
  68. M. E. Carrington, B. A. Meggison, and D. Pickering, 2PI effective action at four loop order in φ4superscript𝜑4{\varphi}^{4}italic_φ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT theory, Phys. Rev. D 94, 025018 (2016).
  69. J. Berges, n𝑛nitalic_n-particle irreducible effective action techniques for gauge theories, Phys. Rev. D 70, 105010 (2004).

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets