- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State

Vanja Marić, Florent Ferro, and Maurizio Fagotti

PDF

Phys. Rev. Lett. 134, 236302 – Published 13 June, 2025

DOI: https://doi.org/10.1103/982k-5jmn

Abstract

We consider translationally invariant quantum spin-12 chains with local interactions and a discrete symmetry that is spontaneously broken at zero temperature. We envision experimenters switching off the couplings between two parts of the system and preparing them in independent equilibrium states. One side of the chain is prepared in a disordered phase, and the other in a symmetry-breaking ground state. When the couplings are switched back on, time evolution ensues. We argue that in integrable systems the front separating the ordered region recedes at the maximal velocity of quasiparticle excitations over the ground state. We infer that, generically, the order parameters should vary on a subdiffusive scale of order t1/3, where t is time, and their fluctuations should exhibit the same scaling. This interfacial region exhibits full range correlations, indicating that it cannot be decomposed into nearly uncorrelated subsystems. Using the transverse-field Ising chain as a case study, we demonstrate that all order parameters follow the same universal scaling functions. Through an analysis of the skew information, we uncover that the breakdown of cluster decomposition has a quantum contribution: each subsystem within the interfacial region, with extent comparable to the region, exists in a macroscopic quantum state.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (90)

  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. C. Gogolin and J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys. 79, 056001 (2016).
  3. M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature (London) 452, 854 (2008).
  4. J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
  5. M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
  6. J. M. Deutsch, Eigenstate thermalization hypothesis, Rep. Prog. Phys. 81, 082001 (2018).
  7. T. Kinoshita, T. Wenger, and D. S. Weiss, A quantum Newton’s cradle, Nature (London) 440, 900 (2006).
  8. S. Hofferberth, I. Lesanovsky, B. Fischer, T. Schumm, and J. Schmiedmayer, Non-equilibrium coherence dynamics in one-dimensional Bose gases, Nature (London) 449, 324 (2007).
  9. M. Gring, M. Kuhnert, T. Langen, T. Kitagawa, B. Rauer, M. Schreitl, I. Mazets, D. A. Smith, E. Demler, and J. Schmiedmayer, Relaxation and prethermalization in an isolated quantum system, Science 337, 1318 (2012).
  10. T. Langen, S. Erne, R. Geiger, B. Rauer, T. Schweigler, M. Kuhnert, W. Rohringer, I. E. Mazets, T. Gasenzer, and J. Schmiedmayer, Experimental observation of a generalized Gibbs ensemble, Science 348, 207 (2015).
  11. M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Relaxation in a completely integrable many-body quantum system: An Ab initio study of the dynamics of the highly excited states of 1D lattice hard-core bosons, Phys. Rev. Lett. 98, 050405 (2007).
  12. B. Doyon, Thermalization and pseudolocality in extended quantum systems, Commun. Math. Phys. 351, 155 (2017).
  13. L. Vidmar and M. Rigol, Generalized Gibbs ensemble in integrable lattice models, J. Stat. Mech. (2016) 064007.
  14. F. H. L. Essler and M. Fagotti, Quench dynamics and relaxation in isolated integrable quantum spin chains, J. Stat. Mech. (2016) 064002.
  15. O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Emergent hydrodynamics in integrable quantum systems out of equilibrium, Phys. Rev. X 6, 041065 (2016).
  16. B. Bertini, M. Collura, J. De Nardis, and M. Fagotti, Transport in out-of-equilibrium XXZ chains: Exact profiles of charges and currents, Phys. Rev. Lett. 117, 207201 (2016).
  17. M. Borsi, B. Pozsgay, and L. Pristyák, Current operators in Bethe Ansatz and generalized hydrodynamics: An exact quantum-classical correspondence, Phys. Rev. X 10, 011054 (2020).
  18. V. Alba, B. Bertini, M. Fagotti, L. Piroli, and P. Ruggiero, Generalized-hydrodynamic approach to inhomogeneous quenches: Correlations, entanglement and quantum effects, J. Stat. Mech. (2021) 114004.
  19. J. D. Nardis, B. Doyon, M. Medenjak, and M. Panfil, Correlation functions and transport coefficients in generalised hydrodynamics, J. Stat. Mech. (2022) 014002.
  20. V. B. Bulchandani, S. Gopalakrishnan, and E. Ilievski, Superdiffusion in spin chains, J. Stat. Mech. (2021) 084001.
  21. M. Borsi, B. Pozsgay, and L. Pristyák, Current operators in integrable models: A review, J. Stat. Mech. (2021) 094001.
  22. F. H. Essler, A short introduction to generalized hydrodynamics, Physica (Amsterdam) 631A, 127572 (2023).
  23. M. Schemmer, I. Bouchoule, B. Doyon, and J. Dubail, Generalized hydrodynamics on an atom chip, Phys. Rev. Lett. 122, 090601 (2019).
  24. N. Malvania, Y. Zhang, Y. Le, J. Dubail, M. Rigol, and D. S. Weiss, Generalized hydrodynamics in strongly interacting 1D Bose gases, Science 373, 1129 (2021).
  25. I. Bouchoule and J. Dubail, Generalized hydrodynamics in the one-dimensional Bose gas: Theory and experiments, J. Stat. Mech. (2022) 014003.
  26. M. Fagotti and F. H. L. Essler, Reduced density matrix after a quantum quench, Phys. Rev. B 87, 245107 (2013).
  27. R. Haag, D. Kastler, and E. B. Trych-Pohlmeyer, Stability and equilibrium states, Commun. Math. Phys. 38, 173 (1974).
  28. L. M. Sieberer, A. Chiocchetta, A. Gambassi, U. C. Täuber, and S. Diehl, Thermodynamic equilibrium as a symmetry of the Schwinger-Keldysh action, Phys. Rev. B 92, 134307 (2015).
  29. Y. Ogata, The stability of the non-equilibrium steady states, Commun. Math. Phys. 245, 577 (2004).
  30. V. Eisler and Z. Rácz, Full counting statistics in a propagating quantum front and random matrix spectra, Phys. Rev. Lett. 110, 060602 (2013).
  31. S. Groha, F. H. L. Essler, and P. Calabrese, Full counting statistics in the transverse field Ising chain, SciPost Phys. 4, 043 (2018).
  32. A. Bastianello and L. Piroli, From the Sinh-Gordon field theory to the one-dimensional Bose gas: Exact local correlations and full counting statistics, J. Stat. Mech. (2018) 113104.
  33. M. Collura and F. H. L. Essler, How order melts after quantum quenches, Phys. Rev. B 101, 041110(R) (2020).
  34. J. Myers, M. J. Bhaseen, R. J. Harris, and B. Doyon, Transport fluctuations in integrable models out of equilibrium, SciPost Phys. 8, 007 (2020).
  35. B. Bertini, P. Calabrese, M. Collura, K. Klobas, and C. Rylands, Nonequilibrium full counting statistics and symmetry-resolved entanglement from space-time duality, Phys. Rev. Lett. 131, 140401 (2023).
  36. R. Senese, J. H. Robertson, and F. H. L. Essler, Out-of-equilibrium full counting statistics in Gaussian theories of quantum magnets, SciPost Phys. 17, 139 (2024).
  37. L. Zadnik, M. Ljubotina, Ž. Krajnik, E. Ilievski, and T. Prosen, Quantum many-body spin ratchets, PRX Quantum 5, 030356 (2024).
  38. B. Doyon, G. Perfetto, T. Sasamoto, and T. Yoshimura, Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems, Phys. Rev. Lett. 131, 027101 (2023).
  39. B. Doyon, G. Perfetto, T. Sasamoto, and T. Yoshimura, Ballistic macroscopic fluctuation theory, SciPost Phys. 15, 136 (2023).
  40. G. D. V. D. Vecchio and B. Doyon, The hydrodynamic theory of dynamical correlation functions in the XX chain, J. Stat. Mech. (2022) 053102.
  41. V. Marić and M. Fagotti, Universality in the tripartite information after global quenches, Phys. Rev. B 108, L161116 (2023).
  42. V. Marić and M. Fagotti, Universality in the tripartite information after global quenches: (Generalised) quantum xy models, J. High Energy Phys. 06 (2023) 140.
  43. V. Marić, Universality in the tripartite information after global quenches: Spin flip and semilocal charges, J. Stat. Mech. (2023) 113103.
  44. Ž. Krajnik, E. Ilievski, and T. Prosen, Absence of normal fluctuations in an integrable magnet, Phys. Rev. Lett. 128, 090604 (2022).
  45. Ž. Krajnik, J. Schmidt, V. Pasquier, E. Ilievski, and T. Prosen, Exact anomalous current fluctuations in a deterministic interacting model, Phys. Rev. Lett. 128, 160601 (2022).
  46. Ž. Krajnik, J. Schmidt, E. Ilievski, and T. Prosen, Dynamical criticality of magnetization transfer in integrable spin chains, Phys. Rev. Lett. 132, 017101 (2024).
  47. T. Yoshimura and i. c. v. Krajnik, Anomalous current fluctuations from Euler hydrodynamics, Phys. Rev. E 111, 024141 (2025).
  48. W. H. Aschbacher and C.-A. Pillet, Non-equilibrium steady states of the XY chain, J. Stat. Phys. 112, 1153 (2003).
  49. L. Piroli, J. De Nardis, M. Collura, B. Bertini, and M. Fagotti, Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions, Phys. Rev. B 96, 115124 (2017).
  50. B. Bertini and L. Piroli, Low-temperature transport in out-of-equilibrium XXZ chains, J. Stat. Mech. (2018) 033104.
  51. B. Bertini, L. Piroli, and P. Calabrese, Universal broadening of the light cone in low-temperature transport, Phys. Rev. Lett. 120, 176801 (2018).
  52. B. Bertini, L. Piroli, and M. Kormos, Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics, Phys. Rev. B 100, 035108 (2019).
  53. L. Bonnes, F. H. L. Essler, and A. M. Läuchli, “Light-Cone” dynamics after quantum quenches in spin chains, Phys. Rev. Lett. 113, 187203 (2014).
  54. H. Spohn, Interacting and noninteracting integrable systems, J. Math. Phys. (N.Y.) 59, 091402 (2018).
  55. M. Collura, A. De Luca, and J. Viti, Analytic solution of the domain-wall nonequilibrium stationary state, Phys. Rev. B 97, 081111(R) (2018).
  56. V. Hunyadi, Z. Rácz, and L. Sasvári, Dynamic scaling of fronts in the quantum XX chain, Phys. Rev. E 69, 066103 (2004).
  57. V. Zauner, M. Ganahl, H. G. Evertz, and T. Nishino, Time evolution within a comoving window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains, J. Phys. Condens. Matter 27, 425602 (2015).
  58. C. A. Tracy and H. Widom, Level-spacing distributions and the Airy kernel, Phys. Lett. B 305, 115 (1993).
  59. T. Platini and D. Karevski, Scaling and front dynamics in Ising quantum chains, Eur. Phys. J. B 48, 225 (2005).
  60. G. Perfetto and A. Gambassi, Ballistic front dynamics after joining two semi-infinite quantum Ising chains, Phys. Rev. E 96, 012138 (2017).
  61. M. Fagotti, Higher-order generalized hydrodynamics in one dimension: The noninteracting test, Phys. Rev. B 96, 220302(R) (2017).
  62. V. B. Bulchandani and C. Karrasch, Subdiffusive front scaling in interacting integrable models, Phys. Rev. B 99, 121410(R) (2019).
  63. B. Bertini, M. Fagotti, L. Piroli, and P. Calabrese, Entanglement evolution and generalised hydrodynamics: Noninteracting systems, J. Phys. A 51, 39LT01 (2018).
  64. V. Alba, B. Bertini, and M. Fagotti, Entanglement evolution and generalised hydrodynamics: Interacting integrable systems, SciPost Phys. 7, 5 (2019).

  65. A quasiparticle with velocity v(p) is in the interfacial region only if v(p)t−vmaxt∼t1/3. Assuming that the second derivative of the velocity with respect to the momentum is nonzero at the maximum, this leads to the condition p−p¯∼t−1/3, where p¯ is the momentum that maximizes the velocity.

  66. S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, England, 2011).
  67. V. Eisler, F. Maislinger, and H. G. Evertz, Universal front propagation in the quantum Ising chain with domain-wall initial states, SciPost Phys. 1, 014 (2016).
  68. V. Eisler and F. Maislinger, Front dynamics in the XY chain after local excitations, SciPost Phys. 8, 37 (2020).
  69. G. Perfetto and A. Gambassi, Dynamics of large deviations in the hydrodynamic limit: Noninteracting systems, Phys. Rev. E 102, 042128 (2020).
  70. A. De Luca, J. Viti, D. Bernard, and B. Doyon, Nonequilibrium thermal transport in the quantum Ising chain, Phys. Rev. B 88, 134301 (2013).
  71. M. Kormos, Inhomogeneous quenches in the transverse field Ising chain: Scaling and front dynamics, SciPost Phys. 3, 020 (2017).
  72. V. Eisler and F. Maislinger, Hydrodynamical phase transition for domain-wall melting in the XY chain, Phys. Rev. B 98, 161117(R) (2018).
  73. M. Fagotti, Locally quasi-stationary states in noninteracting spin chains, SciPost Phys. 8, 48 (2020).
  74. G. Delfino and M. Sorba, Space of initial conditions and universality in nonequilibrium quantum dynamics, Nucl. Phys. B983, 115910 (2022).
  75. S. Bocini, Connected correlations in partitioning protocols: A case study and beyond, SciPost Phys. 15, 027 (2023).
  76. E. H. Lieb and D. W. Robinson, The finite group velocity of quantum spin systems, Commun. Math. Phys. 28, 251 (1972).
  77. S. Bravyi, M. B. Hastings, and F. Verstraete, Lieb-Robinson bounds and the generation of correlations and topological quantum order, Phys. Rev. Lett. 97, 050401 (2006).
  78. V. Marić, F. Ferro, and M. Fagotti, Disorder-order interface propagating over the ferromagnetic ground state in the transverse field Ising chain, Phys. Rev. B 111, 205118 (2025).
  79. E. Bettelheim and P. B. Wiegmann, Universal Fermi distribution of semiclassical nonequilibrium Fermi states, Phys. Rev. B 84, 085102 (2011).
  80. D. S. Dean, P. Le Doussal, S. N. Majumdar, and G. Schehr, Wigner function of noninteracting trapped fermions, Phys. Rev. A 97, 063614 (2018).
  81. H. A. Antosiewicz, Bessel functions of fractional order, in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (National Bureau of Standards, Washington, D.C., 1972).
  82. T. Claeys and A. Doeraene, The generating function for the airy point process and a system of coupled Painlevé II equations, Stud. Appl. Math. 140, 403 (2018).
  83. S. Bocini and M. Fagotti, Growing Schrödinger’s cat states by local unitary time evolution of product states, Phys. Rev. Res. 6, 033108 (2024).
  84. M. Fagotti, Quantum Jamming brings quantum mechanics to macroscopic scales, Phys. Rev. X 14, 021015 (2024).
  85. F. Ferro and M. Fagotti, Kicking quantum Fisher information out of equilibrium, arXiv:2503.21905.
  86. A. J. Leggett, Macroscopic quantum systems and the quantum theory of measurement, Prog. Theor. Phys. Suppl. 69, 80 (1980).
  87. F. Fröwis, P. Sekatski, W. Dür, N. Gisin, and N. Sangouard, Macroscopic quantum states: Measures, fragility, and implementations, Rev. Mod. Phys. 90, 025004 (2018).
  88. G. Tóth and D. Petz, Extremal properties of the variance and the quantum Fisher information, Phys. Rev. A 87, 032324 (2013).
  89. S. Yu, Quantum Fisher information as the convex roof of variance, arXiv:1302.5311.
  90. I. Frérot and T. Roscilde, Quantum variance: A measure of quantum coherence and quantum correlations for many-body systems, Phys. Rev. B 94, 075121 (2016).

Outline

Information

Phys. Rev. Lett. 134, 236302– Published 13 June, 2025
  • Received 15 November 2024
  • Revised 11 April 2025
  • Accepted 23 May 2025
Crossmark - Check for updates button

© 2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation