A nonequilibrium quantum phase transition in strongly coupled spin chains

Eduardo Mascarenhas, Giacomo Giudice, and Vincenzo Savona

Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport phases.

► BibTeX data

► References

[1] S. Sachdev, Quantum phase transitions (Wiley Online Library, 2007).
https://doi.org/10.1017/cbo9780511622540

[2] D. Hirobe, M. Sato, T. Kawamata, Y. Shiomi, K.-i. Uchida, R. Iguchi, Y. Koike, S. Maekawa, and E. Saitoh, Nat. Phys. 13, 30 (2017).
https://doi.org/10.1038/nphys3895

[3] A. Sologubenko, T. Lorenz, H. Ott, and A. Freimuth, J. of Low Temp. Phys. 147, 387 (2007).
https://doi.org/10.1007/s10909-007-9317-x

[4] H. Maeter, A. Zvyagin, H. Luetkens, G. Pascua, Z. Shermadini, R. Saint-Martin, A. Revcolevschi, C. Hess, B. Büchner, and H. Klauss, J. Phys.: Condensed Matter 25, 365601 (2013).
https://doi.org/10.1088/0953-8984/25/36/365601

[5] C. Hess, Eur. Phys. J.-Spec. Top. 151, 73 (2007).
https://doi.org/10.1140/epjst/e2007-00363-8

[6] J.-M. Reiner, M. Marthaler, J. Braumüller, M. Weides, and G. Schön, Phys. Rev. A 94 (2016), 10.1103/​PhysRevA.94.032338.
https://doi.org/10.1103/PhysRevA.94.032338

[7] S. Boixo, T. F. Rønnow, S. V. Isakov, Z. Wang, D. Wecker, D. A. Lidar, J. M. Martinis, and M. Troyer, Nat. Phys. 10, 218 (2014).
https://doi.org/10.1038/nphys2900

[8] A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, et al., Nature 464, 697 (2010).
https://doi.org/10.1038/nature08967

[9] W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, Phys. Rev. Lett. 70, 2253 (1993).
https://doi.org/10.1103/PhysRevLett.70.2253

[10] M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
https://doi.org/10.1038/415039a

[11] G. Roati, C. D'Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
https://doi.org/10.1038/nature07071

[12] C. Schweizer, M. Lohse, R. Citro, and I. Bloch, Phys. Rev. Lett. 117, 170405 (2016).
https://doi.org/10.1103/PhysRevLett.117.170405

[13] M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Science 349, 842 (2015).
https://doi.org/10.1126/science.aaa7432

[14] J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. Hess, P. Hauke, M. Heyl, D. Huse, and C. Monroe, Nat. Phys. 12, 907 (2016).
https://doi.org/10.1038/nphys3783

[15] S. Hild, T. Fukuhara, P. Schauß, J. Zeiher, M. Knap, E. Demler, I. Bloch, and C. Gross, Phys. Rev. Lett. 113, 147205 (2014).
https://doi.org/10.1103/PhysRevLett.113.147205

[16] S. Hild, T. Fukuhara, P. Schauß, J. Zeiher, M. Knap, E. Demler, I. Bloch, and C. Gross, Nature 502, 76 (2013).
https://doi.org/10.1038/nature12541

[17] T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schausz, S. Hild, D. Bellem, U. Schollwock, T. Giamarchi, C. Gross, I. Bloch, and S. Kuhr, Nat. Phys. 9, 235 (2013).
https://doi.org/10.1038/nphys2561

[18] S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A. M. Rey, A. Polkovnikov, E. A. Demler, M. D. Lukin, and I. Bloch, Science 319, 235 (2008).
https://doi.org/10.1126/science.1150841

[19] J. Simon, W. S. Bakr, R. Ma, M. E. Tai, P. M. Preiss, and M. Greiner, Nature 472, 307 (2011).
https://doi.org/10.1038/nature09994

[20] M. Boll, T. A. Hilker, G. Salomon, A. Omran, J. Nespolo, L. Pollet, I. Bloch, and C. Gross, Science 353, 1257 (2016).
https://doi.org/10.1126/science.aag1635

[21] L. Vidmar, J. P. Ronzheimer, M. Schreiber, S. Braun, S. S. Hodgman, S. Langer, F. Heidrich-Meisner, I. Bloch, and U. Schneider, Phys. Rev. Lett. 115, 175301 (2015).
https://doi.org/10.1103/PhysRevLett.115.175301

[22] J. P. Ronzheimer, M. Schreiber, S. Braun, S. S. Hodgman, S. Langer, I. P. McCulloch, F. Heidrich-Meisner, I. Bloch, and U. Schneider, Phys. Rev. Lett. 110, 205301 (2013).
https://doi.org/10.1103/PhysRevLett.110.205301

[23] B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, Nature 501 (2013), 10.1038/​nature12483.
https://doi.org/10.1038/nature12483

[24] A. V. Gorshkov, S. R. Manmana, G. Chen, J. Ye, E. Demler, M. D. Lukin, and A. M. Rey, Phys. Rev. Lett. 107, 115301 (2011a).
https://doi.org/10.1103/PhysRevLett.107.115301

[25] A. V. Gorshkov, S. R. Manmana, G. Chen, E. Demler, M. D. Lukin, and A. M. Rey, Phys. Rev. A 84, 033619 (2011b).
https://doi.org/10.1103/PhysRevA.84.033619

[26] X. Zotos, F. Naef, and P. Prelovsek, Phys. Rev. B 55, 11029 (1997).
https://doi.org/10.1103/PhysRevB.55.11029

[27] T. Prosen, Phys. Rev. Lett. 106, 217206 (2011a).
https://doi.org/10.1103/PhysRevLett.106.217206

[28] T. Prosen and E. Ilievski, Phys. Rev. Lett. 111, 057203 (2013).
https://doi.org/10.1103/PhysRevLett.111.057203

[29] R. Steinigeweg and J. Gemmer, Phys. Rev. B 80, 184402 (2009).
https://doi.org/10.1103/PhysRevB.80.184402

[30] R. Steinigeweg and W. Brenig, Phys. Rev. Lett. 107, 250602 (2011).
https://doi.org/10.1103/PhysRevLett.107.250602

[31] T. Antal, Z. Rácz, A. Rákos, and G. M. Schütz, Phys. Rev. E 59, 4912 (1999).
https://doi.org/10.1103/PhysRevE.59.4912

[32] T. Antal, Z. Rácz, A. Rákos, and G. M. Schütz, Phys. Rev. E 57, 5184 (1998).
https://doi.org/10.1103/PhysRevE.57.5184

[33] J. Lancaster and A. Mitra, Phys. Rev. E 81, 061134 (2010).
https://doi.org/10.1103/PhysRevE.81.061134

[34] D. Gobert, C. Kollath, U. Schollwöck, and G. Schütz, Phys. Rev. E 71, 036102 (2005).
https://doi.org/10.1103/PhysRevE.71.036102

[35] J. Marino and S. Diehl, Phys. Rev. Lett. 116, 070407 (2016).
https://doi.org/10.1103/PhysRevLett.116.070407

[36] M. J. Hartmann, J. Opt. 18, 104005 (2016).
https://doi.org/10.1088/2040-8978/18/10/104005

[37] J. Wang and G. Casati, Phys. Rev. Lett. 118, 040601 (2017).
https://doi.org/10.1103/PhysRevLett.118.040601

[38] M. Žnidarič, Phys. Rev. Lett. 106, 220601 (2011).
https://doi.org/10.1103/PhysRevLett.106.220601

[39] T. Prosen, Phys. Rev. Lett. 107, 137201 (2011b).
https://doi.org/10.1103/PhysRevLett.107.137201

[40] R. Steinigeweg, M. Ogiewa, and J. Gemmer, Europhys. Lett.) 87, 10002 (2009).
https://doi.org/10.1209/0295-5075/87/10002

[41] J. J. Mendoza-Arenas, S. R. Clark, and D. Jaksch, Phys. Rev. E 91, 042129 (2015).
https://doi.org/10.1103/PhysRevE.91.042129

[42] J. J. Mendoza-Arenas, T. Grujic, D. Jaksch, and S. R. Clark, Phys. Rev. B 87, 235130 (2013).
https://doi.org/10.1103/PhysRevB.87.235130

[43] G. Benenti, G. Casati, T. Prosen, D. Rossini, and M. Žnidarič, Phys. Rev. B 80, 035110 (2009a).
https://doi.org/10.1103/PhysRevB.80.035110

[44] G. Benenti, G. Casati, T. Prosen, and D. Rossini, Europhys. Lett 85, 37001 (2009b).
https://doi.org/10.1209/0295-5075/85/37001

[45] H.-P. Breuer and F. Petruccione, The theory of open quantum systems (Oxford University Press, 2002).

[46] I. de Vega and D. Alonso, Rev. Mod. Phys. 89, 015001 (2017).
https://doi.org/10.1103/RevModPhys.89.015001

[47] A. De Luca, M. Collura, and J. De Nardis, Phys. Rev. B 96, 020403 (2017).
https://doi.org/10.1103/PhysRevB.96.020403

[48] M. Ljubotina, M. Žnidarič, and T. Prosen, Nature Commun. 8 (2017), 10.1038/​ncomms16117.
https://doi.org/10.1038/ncomms16117

[49] L. Bonnes, F. H. Essler, and A. M. Läuchli, Phys. Rev. Lett. 113, 187203 (2014).
https://doi.org/10.1103/PhysRevLett.113.187203

[50] V. Alba and F. Heidrich-Meisner, Phys. Rev. B 90, 075144 (2014).
https://doi.org/10.1103/PhysRevB.90.075144

[51] T. Sabetta and G. Misguich, Phys. Rev. B 88, 245114 (2013).
https://doi.org/10.1103/PhysRevB.88.245114

[52] A. De Luca, J. Viti, L. Mazza, and D. Rossini, Phys. Rev. B 90, 161101(R) (2014).
https://doi.org/10.1103/PhysRevB.90.161101

[53] M. Collura and G. Martelloni, J. Stat. Mech. 2014, P08006 (2014).
https://doi.org/10.1088/1742-5468/2014/08/P08006

[54] A. Biella, A. De Luca, J. Viti, D. Rossini, L. Mazza, and R. Fazio, Phys. Rev. B 93, 205121 (2016).
https://doi.org/10.1103/PhysRevB.93.205121

[55] C. Karrasch, R. Ilan, and J. Moore, Phys. Rev. B 88, 195129 (2013).
https://doi.org/10.1103/PhysRevB.88.195129

[56] M. Collura and D. Karevski, Phys. Rev. B 89, 214308 (2014).
https://doi.org/10.1103/PhysRevB.89.214308

[57] C.-C. Chien, M. Di Ventra, and M. Zwolak, Phys. Rev. A 90, 023624 (2014).
https://doi.org/10.1103/PhysRevA.90.023624

[58] B. Bertini, M. Collura, J. De Nardis, and M. Fagotti, Phys Rev. Lett. 117, 207201 (2016).
https://doi.org/10.1103/PhysRevLett.117.207201

[59] O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Phys. Rev. X 6 (2016), 10.1103/​PhysRevX.6.041065.
https://doi.org/10.1103/PhysRevX.6.041065

[60] C. Karrasch, J. Moore, and F. Heidrich-Meisner, Phys. Rev. B 89, 075139 (2014).
https://doi.org/10.1103/PhysRevB.89.075139

[61] P. S. Alexander Branschädel, Guenter Schneider, arXiv:1004.4178 (2010).
arXiv:1004.4178

[62] I. de Vega, U. Schollwöck, and F. A. Wolf, Phys. Rev. B 92, 155126 (2015).
https://doi.org/10.1103/PhysRevB.92.155126

[63] J. Prior, A. W. Chin, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 105, 050404 (2010).
https://doi.org/10.1103/PhysRevLett.105.050404

[64] A. Rivas and M. A. Martin-Delgado, Scientific Reports 7, 6350 (2017).
https://doi.org/10.1038/s41598-017-06722-x

[65] M. Mitchison and M. Plenio, arXiv:1708.05574 (2017).
arXiv:1708.05574

[66] S. Sotiriadis, Phys. Rev. A 94, 031605 (2016).
https://doi.org/10.1103/PhysRevA.94.031605

[67] U. Schollwöck, Ann. of Phys. 326, 96 (2011).
https://doi.org/10.1016/j.aop.2010.09.012

[68] F. Verstraete, V. Murg, and J. I. Cirac, Adv. Phys. 57, 143 (2008).
https://doi.org/10.1080/14789940801912366

[69] M. Žnidarič, A. Scardicchio, and V. K. Varma, Phys. Rev. Lett. 117, 040601 (2016).
https://doi.org/10.1103/PhysRevLett.117.040601

[70] H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009).
https://doi.org/10.1103/PhysRevLett.103.210401

► Cited by (beta)

[1] Chu Guo, Ines de Vega, Ulrich Schollwöck, Dario Poletti, "Stable-unstable transition for a Bose-Hubbard chain coupled to an environment", Physical Review A 97, 053610 (2018).

[2] Wim Casteels, Ryan M. Wilson, Michiel Wouters, "Gutzwiller Monte Carlo approach for a critical dissipative spin model", Physical Review A 97, 062107 (2018).

[3] Vincenzo Alba, "Entanglement and quantum transport in integrable systems", Physical Review B 97, 245135 (2018).

[4] Pooja Manasi, Dibyendu Roy, "Light propagation through one-dimensional interacting open quantum systems", Physical Review A 98, 023802 (2018).

(The above data is from Crossref's cited-by service. Unfortunately not all publishers provide suitable and complete citation data so that some citing works or bibliographic details may be missing.)