Dynamical many-body delocalization transition of a Tonks gas in a quasi-periodic driving potential

Vincent Vuatelet; Adam Rançon

doi:10.22331/q-2023-02-09-917

Dynamical many-body delocalization transition of a Tonks gas in a quasi-periodic driving potential

Vincent Vuatelet and Adam Rançon

Univ. Lille, CNRS, UMR 8523 – PhLAM – Laboratoire de Physique des Lasers, Atomes et Molécules, F-59000 Lille, France

Published:	2023-02-09, volume 7, page 917
Eprint:	arXiv:2209.12510v2
Doi:	https://doi.org/10.22331/q-2023-02-09-917
Citation:	Quantum 7, 917 (2023).

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Abstract

The quantum kicked rotor is well-known for displaying dynamical (Anderson) localization. It has recently been shown that a periodically kicked Tonks gas will always localize and converge to a finite energy steady-state. This steady-state has been described as being effectively thermal with an effective temperature that depends on the parameters of the kick. Here we study a generalization to a quasi-periodic driving with three frequencies which, without interactions, has a metal-insulator Anderson transition. We show that a quasi-periodically kicked Tonks gas goes through a dynamical many-body delocalization transition when the kick strength is increased. The localized phase is still described by a low effective temperature, while the delocalized phase corresponds to an infinite-temperature phase, with the temperature increasing linearly in time. At the critical point, the momentum distribution of the Tonks gas displays different scaling at small and large momenta (contrary to the non-interacting case), signaling a breakdown of the one-parameter scaling theory of localization.

► BibTeX data

@article{Vuatelet2023dynamicalmanybody,
  doi = {10.22331/q-2023-02-09-917},
  url = {https://doi.org/10.22331/q-2023-02-09-917},
  title = {Dynamical many-body delocalization transition of a {T}onks gas in a quasi-periodic driving potential},
  author = {Vuatelet, Vincent and Ran{\c{c}}on, Adam},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {917},
  month = feb,
  year = {2023}
}

► References

[1] P. W. Anderson, Phys. Rev. 109, 1492 (1958).
https://doi.org/10.1103/PhysRev.109.1492

[2] F. Evers and A. D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008).
https://doi.org/10.1103/RevModPhys.80.1355

[3] S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982).
https://doi.org/10.1103/PhysRevLett.49.509

[4] D. Shepelyansky, Physica D: Nonlinear Phenomena 28, 103 (1987).
https://doi.org/10.1016/0167-2789(87)90123-0

[5] G. Casati, I. Guarneri, and D. L. Shepelyansky, Phys. Rev. Lett. 62, 345 (1989).
https://doi.org/10.1103/PhysRevLett.62.345

[6] J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, Phys. Rev. Lett. 101, 255702 (2008).
https://doi.org/10.1103/PhysRevLett.101.255702

[7] G. Lemarié, J. Chabé, P. Szriftgiser, J. C. Garreau, B. Grémaud, and D. Delande, Phys. Rev. A 80, 043626 (2009).
https://doi.org/10.1103/PhysRevA.80.043626

[8] G. Lemarié, H. Lignier, D. Delande, P. Szriftgiser, and J. C. Garreau, Phys. Rev. Lett. 105, 090601 (2010).
https://doi.org/10.1103/PhysRevLett.105.090601

[9] M. Lopez, J.-F. Clément, P. Szriftgiser, J. C. Garreau, and D. Delande, Phys. Rev. Lett. 108, 095701 (2012).
https://doi.org/10.1103/PhysRevLett.108.095701

[10] I. Manai, J.-F. Clément, R. Chicireanu, C. Hainaut, J. C. Garreau, P. Szriftgiser, and D. Delande, Phys. Rev. Lett. 115, 240603 (2015).
https://doi.org/10.1103/PhysRevLett.115.240603

[11] R. Nandkishore, Phys. Rev. B 92, 245141 (2015).
https://doi.org/10.1103/PhysRevB.92.245141

[12] D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Rev. Mod. Phys. 91, 021001 (2019).
https://doi.org/10.1103/RevModPhys.91.021001

[13] M. Serbyn, Z. Papić, and D. A. Abanin, Phys. Rev. Lett. 111, 127201 (2013).
https://doi.org/10.1103/PhysRevLett.111.127201

[14] D. A. Huse, R. Nandkishore, and V. Oganesyan, Phys. Rev. B 90, 174202 (2014).
https://doi.org/10.1103/PhysRevB.90.174202

[15] P. Ponte, Z. Papić, F. m. c. Huveneers, and D. A. Abanin, Phys. Rev. Lett. 114, 140401 (2015a).
https://doi.org/10.1103/PhysRevLett.114.140401

[16] P. Ponte, A. Chandran, Z. Papić, and D. A. Abanin, Annals of Physics 353, 196 (2015b).
https://doi.org/10.1016/j.aop.2014.11.008

[17] S. Adachi, M. Toda, and K. Ikeda, Phys. Rev. Lett. 61, 659 (1988).
https://doi.org/10.1103/PhysRevLett.61.659

[18] Z. Wen-Lei and J. Quan-Lin, Communications in Theoretical Physics 51, 465 (2009).
https://doi.org/10.1088/0253-6102/51/3/17

[19] A. C. Keser, S. Ganeshan, G. Refael, and V. Galitski, Phys. Rev. B 94, 085120 (2016).
https://doi.org/10.1103/PhysRevB.94.085120

[20] E. B. Rozenbaum and V. Galitski, Phys. Rev. B 95, 064303 (2017).
https://doi.org/10.1103/PhysRevB.95.064303

[21] S. Notarnicola, F. Iemini, D. Rossini, R. Fazio, A. Silva, and A. Russomanno, Phys. Rev. E 97, 022202 (2018).
https://doi.org/10.1103/PhysRevE.97.022202

[22] S. Notarnicola, A. Silva, R. Fazio, and A. Russomanno, Journal of Statistical Mechanics: Theory and Experiment 2020, 024008 (2020).
https://doi.org/10.1088/1742-5468/ab6de4

[23] P. Qin, A. Andreanov, H. C. Park, and S. Flach, Scientific Reports 7, 41139 (2017).
https://doi.org/10.1038/srep41139

[24] C. Rylands, E. B. Rozenbaum, V. Galitski, and R. Konik, Phys. Rev. Lett. 124, 155302 (2020).
https://doi.org/10.1103/PhysRevLett.124.155302

[25] R. Chicireanu and A. Rançon, Phys. Rev. A 103, 043314 (2021).
https://doi.org/10.1103/PhysRevA.103.043314

[26] V. Vuatelet and A. Rançon, Phys. Rev. A 104, 043302 (2021).
https://doi.org/10.1103/PhysRevA.104.043302

[27] D. L. Shepelyansky, Phys. Rev. Lett. 70, 1787 (1993).
https://doi.org/10.1103/PhysRevLett.70.1787

[28] A. S. Pikovsky and D. L. Shepelyansky, Phys. Rev. Lett. 100, 094101 (2008).
https://doi.org/10.1103/PhysRevLett.100.094101

[29] S. Flach, D. O. Krimer, and C. Skokos, Phys. Rev. Lett. 102, 024101 (2009).
https://doi.org/10.1103/PhysRevLett.102.024101

[30] G. Gligorić , J. D. Bodyfelt, and S. Flach, EPL (Europhysics Letters) 96, 30004 (2011).
https://doi.org/10.1209/0295-5075/96/30004

[31] N. Cherroret, B. Vermersch, J. C. Garreau, and D. Delande, Phys. Rev. Lett. 112, 170603 (2014).
https://doi.org/10.1103/PhysRevLett.112.170603

[32] S. Lellouch, A. Rançon, S. De Bièvre, D. Delande, and J. C. Garreau, Phys. Rev. A 101, 043624 (2020).
https://doi.org/10.1103/PhysRevA.101.043624

[33] M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol, Rev. Mod. Phys. 83, 1405 (2011).
https://doi.org/10.1103/revmodphys.83.1405

[34] A. Cao, R. Sajjad, H. Mas, E. Q. Simmons, J. L. Tanlimco, E. Nolasco-Martinez, T. Shimasaki, H. E. Kondakci, V. Galitski, and D. M. Weld, Nature Physics 18, 1302 (2022).
https://doi.org/10.1038/s41567-022-01724-7

[35] J. H. See Toh, K. C. McCormick, X. Tang, Y. Su, X.-W. Luo, C. Zhang, and S. Gupta, Nature Physics 18, 1297 (2022).
https://doi.org/10.1038/s41567-022-01721-w

[36] L. Ermann and D. L. Shepelyansky, Journal of Physics A: Mathematical and Theoretical 47, 335101 (2014).
https://doi.org/10.1088/1751-8113/47/33/335101

[37] B. Vermersch, D. Delande, and J. C. Garreau, Phys. Rev. A 101, 053625 (2020).
https://doi.org/10.1103/PhysRevA.101.053625

[38] K. Slevin and T. Ohtsuki, Phys. Rev. Lett. 82, 382 (1999).
https://doi.org/10.1103/PhysRevLett.82.382

[39] E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
https://doi.org/10.1103/PhysRevLett.42.673

[40] P. Wölfle and D. Vollhardt, International Journal of Modern Physics B 24, 1526 (2010).
https://doi.org/10.1142/S0217979210064502

[41] M. Lopez, J.-F. Clément, G. Lemarié, D. Delande, P. Szriftgiser, and J. C. Garreau, New Journal of Physics 15, 065013 (2013).
https://doi.org/10.1088/1367-2630/15/6/065013

[42] A. Rodriguez, L. J. Vasquez, K. Slevin, and R. A. Römer, Phys. Rev. B 84, 134209 (2011).
https://doi.org/10.1103/PhysRevB.84.134209

[43] P. Akridas-Morel, N. Cherroret, and D. Delande, Phys. Rev. A 100, 043612 (2019).
https://doi.org/10.1103/PhysRevA.100.043612

[44] J. Chalker, Physica A: Statistical Mechanics and its Applications 167, 253 (1990).
https://doi.org/10.1016/0378-4371(90)90056-X

[45] M. Girardeau, Journal of Mathematical Physics 1, 516 (1960).
https://doi.org/10.1063/1.1703687

[46] A. Lenard, Journal of Mathematical Physics 5, 930 (1964).
https://doi.org/10.1063/1.1704196

[47] H. Buljan, R. Pezer, and T. Gasenzer, Phys. Rev. Lett. 100, 080406 (2008).
https://doi.org/10.1103/PhysRevLett.100.080406

[48] D. Jukić, R. Pezer, T. Gasenzer, and H. Buljan, Phys. Rev. A 78, 053602 (2008).
https://doi.org/10.1103/PhysRevA.78.053602

[49] R. Pezer, T. Gasenzer, and H. Buljan, Phys. Rev. A 80, 053616 (2009).
https://doi.org/10.1103/PhysRevA.80.053616

[50] M. Rigol and A. Muramatsu, Phys. Rev. Lett. 94, 240403 (2005a).
https://doi.org/10.1103/PhysRevLett.94.240403

[51] M. Rigol and A. Muramatsu, Phys. Rev. A 72, 013604 (2005b).
https://doi.org/10.1103/PhysRevA.72.013604

[52] M. Olshanii and V. Dunjko, Phys. Rev. Lett. 91, 090401 (2003).
https://doi.org/10.1103/physrevlett.91.090401

[53] S. Tan, Annals of Physics 323, 2971 (2008).
https://doi.org/10.1016/j.aop.2008.03.005

[54] P. Vignolo and A. Minguzzi, Phys. Rev. Lett. 110, 020403 (2013).
https://doi.org/10.1103/physrevlett.110.020403

[55] A. Its, A. Izergin, and V. Korepin, Physica D: Nonlinear Phenomena 53, 187 (1991).
https://doi.org/10.1016/0167-2789(91)90171-5

[56] M. Rigol, Phys. Rev. A 72, 063607 (2005).
https://doi.org/10.1103/PhysRevA.72.063607

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[3] Ang Yang, Zekai Chen, Yanliang Guo, Manuele Landini, Hanns-Christoph Nägerl, and Lei Ying, "Origin and Emergent Features of Many-Body Dynamical Localization", Physical Review Letters 136 12, 123402 (2026).

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[5] Anjali Nambudiripad, J. Bharathi Kannan, and M. S. Santhanam, "Chaos and localized phases in a two-body linear kicked rotor system", Physical Review E 109 3, 034206 (2024).

[6] Ang Yang, Yue Chen, and Lei Ying, "Temperature effect on a kicked Tonks-Girardeau gas", Physical Review A 113 5, 053302 (2026).

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