Abstract
We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write down and solve the Bethe equations for the generalized quantum model and show that these take on a particularly simple form that allows for an exact solution: Essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly, providing an exact description of interacting chiral particles in the thermodynamic limit. Although the model is interacting, its unusually simple structure allows us to construct operators that spread with no butterfly effect; this construction does not seem possible in other interacting integrable systems. This model exemplifies a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.
Original language | English (US) |
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Article number | 170603 |
Journal | Physical review letters |
Volume | 123 |
Issue number | 17 |
DOIs | |
State | Published - Oct 23 2019 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
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In: Physical review letters, Vol. 123, No. 17, 170603, 23.10.2019.
Research output: Contribution to journal › Article › peer-review
TY - JOUR
T1 - Integrable many-body quantum floquet-thouless pumps
AU - Friedman, Aaron J.
AU - Gopalakrishnan, Sarang
AU - Vasseur, Romain
N1 - Funding Information: In summary, we present and solve exactly a Floquet model that is the first of its kind in a number of respects. It is the first example of an interacting integrable Floquet model that is neither smoothly deformable to Hamiltonian dynamics [66] nor classically simulable (FFA). Our solution of the dispersing model has provided insight into the physics of the FFA model, which prior to this work was not confirmed to be integrable in the Yang-Baxter sense. The dispersing model regularizes several pathological features of the FFA model, but nonetheless preserves the chiral quasiparticle excitations of the FFA model, which realize topological Thouless pumping. Despite the complicated nature of the Hamiltonian terms, the resulting Bethe (4) and TBA equations (8) are the simplest of any interacting integrable model as far as we are aware. This model shows the existence of interacting Floquet models with stable chiral quasiparticles and suggests a route to finding others, building on integrable cellular automata [67,71,109,110] . Finally, we briefly discuss the experimental implications of this Letter. The FFA model comprises standard cnot and Toffoli gates and is therefore simple to implement on existing “noisy intermediate-scale quantum computers” [111] based on ion traps, cold atoms, or superconducting qubits. The Hamiltonian (2) is more challenging, although a Trotterized version that preserves integrability may be implemented on small gate-based quantum simulators; transport, operator growth [112] , and even level statistics [113] have been measured in this setting. There might also be simpler-to-realize deformations of the FFA model that retain integrability (e.g., models that only contain the doublon-hopping term). Exploring such deformations is an interesting topic for future work. We thank D. Huse, V. Khemani, A. Nahum, T. Prosen, and B. Ware for illuminating discussions. This research was supported by the National Science Foundation via Grants No. DGE-1321846 (Graduate Research Fellowship Program, A. J. F.), No. DMR-1455366 (A. J. F.), and No. DMR-1653271 (S. G.); and the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Early Career Award No. DE-SC0019168 (R. V.). [1] 1 A. Eckardt , Rev. Mod. Phys. 89 , 011004 ( 2017 ). RMPHAT 0034-6861 10.1103/RevModPhys.89.011004 [2] 2 M. Bukov , L. D’Alessio , and A. Polkovnikov , Adv. Phys. 64 , 139 ( 2015 ). ADPHAH 0001-8732 10.1080/00018732.2015.1055918 [3] 3 F. Meinert , M. J. Mark , K. Lauber , A. J. Daley , and H.-C. Nägerl , Phys. Rev. Lett. 116 , 205301 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.116.205301 [4] 4 M. Holthaus , J. Phys. B 49 , 013001 ( 2016 ). JPAPEH 0953-4075 10.1088/0953-4075/49/1/013001 [5] 5 N. Goldman and J. Dalibard , Phys. Rev. X 4 , 031027 ( 2014 ). PRXHAE 2160-3308 10.1103/PhysRevX.4.031027 [6] 6 T. Kitagawa , E. Berg , M. Rudner , and E. Demler , Phys. Rev. B 82 , 235114 ( 2010 ). PRBMDO 1098-0121 10.1103/PhysRevB.82.235114 [7] 7 N. H. Lindner , G. Refael , and V. Galitski , Nat. Phys. 7 , 490 ( 2011 ). NPAHAX 1745-2473 10.1038/nphys1926 [8] 8 M. S. Rudner , N. H. Lindner , E. Berg , and M. Levin , Phys. Rev. X 3 , 031005 ( 2013 ). PRXHAE 2160-3308 10.1103/PhysRevX.3.031005 [9] 9 F. Nathan and M. S. Rudner , New J. Phys. 17 , 125014 ( 2015 ). NJOPFM 1367-2630 10.1088/1367-2630/17/12/125014 [10] 10 T. Oka and H. Aoki , Phys. Rev. B 79 , 081406(R) ( 2009 ). PRBMDO 1098-0121 10.1103/PhysRevB.79.081406 [11] 11 F. Görg , M. Messer , K. Sandholzer , G. Jotzu , R. Desbuquois , and T. Esslinger , Nature (London) 553 , 481 ( 2018 ). NATUAS 0028-0836 10.1038/nature25135 [12] 12 M. Bukov , M. Kolodrubetz , and A. Polkovnikov , Phys. Rev. Lett. 116 , 125301 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.116.125301 [13] 13 F. Harper , R. Roy , M. S. Rudner , and S. L. Sondhi , arXiv:1905.01317 . [14] 14 T. Prosen , Phys. Rev. E 60 , 3949 ( 1999 ). PLEEE8 1063-651X 10.1103/PhysRevE.60.3949 [15] 15 T. Prosen , Prog. Theor. Phys. Suppl. 139 , 191 ( 2000 ). PTPSEP 0375-9687 10.1143/PTPS.139.191 [16] 16 Y. Wang , H. Steinberg , P. Jarillo-Herrero , and N. Gedik , Science 342 , 453 ( 2013 ). SCIEAS 0036-8075 10.1126/science.1239834 [17] 17 M. Aidelsburger , M. Atala , M. Lohse , J. T. Barreiro , B. Paredes , and I. Bloch , Phys. Rev. Lett. 111 , 185301 ( 2013 ). PRLTAO 0031-9007 10.1103/PhysRevLett.111.185301 [18] 18 H. Miyake , G. A. Siviloglou , C. J. Kennedy , W. C. Burton , and W. Ketterle , Phys. Rev. Lett. 111 , 185302 ( 2013 ). PRLTAO 0031-9007 10.1103/PhysRevLett.111.185302 [19] 19 G. Jotzu , M. Messer , R. Desbuquois , M. Lebrat , T. Uehlinger , D. Greif , and T. Esslinger , Nature (London) 515 , 237 ( 2014 ). NATUAS 0028-0836 10.1038/nature13915 [20] 20 Z. Gu , H. A. Fertig , D. P. Arovas , and A. Auerbach , Phys. Rev. Lett. 107 , 216601 ( 2011 ). PRLTAO 0031-9007 10.1103/PhysRevLett.107.216601 [21] 21 T. Kitagawa , T. Oka , A. Brataas , L. Fu , and E. Demler , Phys. Rev. B 84 , 235108 ( 2011 ). PRBMDO 1098-0121 10.1103/PhysRevB.84.235108 [22] 22 V. Khemani , A. Lazarides , R. Moessner , and S. L. Sondhi , Phys. Rev. Lett. 116 , 250401 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.116.250401 [23] 23 C. W. von Keyserlingk , V. Khemani , and S. L. Sondhi , Phys. Rev. B 94 , 085112 ( 2016 ). PRBMDO 2469-9950 10.1103/PhysRevB.94.085112 [24] 24 D. V. Else , B. Bauer , and C. Nayak , Phys. Rev. Lett. 117 , 090402 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.117.090402 [25] 25 D. V. Else , B. Bauer , and C. Nayak , Phys. Rev. X 7 , 011026 ( 2017 ). PRXHAE 2160-3308 10.1103/PhysRevX.7.011026 [26] 26 N. Y. Yao , A. C. Potter , I.-D. Potirniche , and A. Vishwanath , Phys. Rev. Lett. 118 , 030401 ( 2017 ). PRLTAO 0031-9007 10.1103/PhysRevLett.118.030401 [27] 27 W. W. Ho , S. Choi , M. D. Lukin , and D. A. Abanin , Phys. Rev. Lett. 119 , 010602 ( 2017 ). PRLTAO 0031-9007 10.1103/PhysRevLett.119.010602 [28] 28 J. Zhang , P. W. Hess , A. Kyprianidis , P. Becker , A. Lee , J. Smith , G. Pagano , I. D. Potirniche , A. C. Potter , A. Vishwanath , N. Y. Yao , and C. Monroe , Nature (London) 543 , 217 ( 2017 ). NATUAS 0028-0836 10.1038/nature21413 [29] 29 S. Choi , J. Choi , R. Landig , G. Kucsko , H. Zhou , J. Isoya , F. Jelezko , S. Onoda , H. Sumiya , V. Khemani , C. von Keyserlingk , N. Y. Yao , E. Demler , and M. D. Lukin , Nature (London) 543 , 221 ( 2017 ). NATUAS 0028-0836 10.1038/nature21426 [30] 30 P. Titum , N. H. Lindner , M. C. Rechtsman , and G. Refael , Phys. Rev. Lett. 114 , 056801 ( 2015 ). PRLTAO 0031-9007 10.1103/PhysRevLett.114.056801 [31] 31 P. Titum , E. Berg , M. S. Rudner , G. Refael , and N. H. Lindner , Phys. Rev. X 6 , 021013 ( 2016 ). PRXHAE 2160-3308 10.1103/PhysRevX.6.021013 [32] 32 D. J. Thouless , Phys. Rev. B 27 , 6083 ( 1983 ). PRBMDO 0163-1829 10.1103/PhysRevB.27.6083 [33] 33 N. H. Lindner , E. Berg , and M. S. Rudner , Phys. Rev. X 7 , 011018 ( 2017 ). PRXHAE 2160-3308 10.1103/PhysRevX.7.011018 [34] 34 T. Kuwahara , T. Mori , and K. Saito , Ann. Phys. (Amsterdam) 367 , 96 ( 2016 ). APNYA6 0003-4916 10.1016/j.aop.2016.01.012 [35] 35 D. A. Abanin , W. De Roeck , and F. Huveneers , Phys. Rev. Lett. 115 , 256803 ( 2015 ). PRLTAO 0031-9007 10.1103/PhysRevLett.115.256803 [36] 36 D. Basko , I. Aleiner , and B. Altshuler , Ann. Phys. (Amsterdam) 321 , 1126 ( 2006 ). APNYA6 0003-4916 10.1016/j.aop.2005.11.014 [37] 37 V. Oganesyan and D. A. Huse , Phys. Rev. B 75 , 155111 ( 2007 ). PRBMDO 1098-0121 10.1103/PhysRevB.75.155111 [38] 38 A. Pal and D. A. Huse , Phys. Rev. B 82 , 174411 ( 2010 ). PRBMDO 1098-0121 10.1103/PhysRevB.82.174411 [39] 39 R. Nandkishore and D. A. Huse , Annu. Rev. Condens. Matter Phys. 6 , 15 ( 2015 ). ARCMCX 1947-5454 10.1146/annurev-conmatphys-031214-014726 [40] 40 E. Altman and R. Vosk , Annu. Rev. Condens. Matter Phys. 6 , 383 ( 2015 ). ARCMCX 1947-5454 10.1146/annurev-conmatphys-031214-014701 [41] 41 R. Vasseur and J. E. Moore , J. Stat. Mech. ( 2016 ) 064010 . JSMTC6 1742-5468 10.1088/1742-5468/2016/06/064010 [42] 42 D. A. Abanin , E. Altman , I. Bloch , and M. Serbyn , Rev. Mod. Phys. 91 , 021001 ( 2019 ). RMPHAT 0034-6861 10.1103/RevModPhys.91.021001 [43] 43 A. Lazarides , A. Das , and R. Moessner , Phys. Rev. Lett. 115 , 030402 ( 2015 ). PRLTAO 0031-9007 10.1103/PhysRevLett.115.030402 [44] 44 D. A. Huse , R. Nandkishore , V. Oganesyan , A. Pal , and S. L. Sondhi , Phys. Rev. B 88 , 014206 ( 2013 ). PRBMDO 1098-0121 10.1103/PhysRevB.88.014206 [45] 45 Y. Bahri , R. Vosk , E. Altman , and A. Vishwanath , Nat. Commun. 6 , 7341 ( 2015 ). NCAOBW 2041-1723 10.1038/ncomms8341 [46] 46 B. Bauer and C. Nayak , J. Stat. Mech. ( 2013 ) P09005 . JSMTC6 1742-5468 10.1088/1742-5468/2013/09/P09005 [47] 47 T. Prosen , Phys. Rev. Lett. 80 , 1808 ( 1998 ). PRLTAO 0031-9007 10.1103/PhysRevLett.80.1808 [48] 48 P. Ponte , Z. Papić , F. Huveneers , and D. A. Abanin , Phys. Rev. Lett. 114 , 140401 ( 2015 ). PRLTAO 0031-9007 10.1103/PhysRevLett.114.140401 [49] 49 C. W. von Keyserlingk and S. L. Sondhi , Phys. Rev. B 93 , 245145 ( 2016 ). PRBMDO 2469-9950 10.1103/PhysRevB.93.245145 [50] 50 C. W. von Keyserlingk and S. L. Sondhi , Phys. Rev. B 93 , 245146 ( 2016 ). PRBMDO 2469-9950 10.1103/PhysRevB.93.245146 [51] 51 D. V. Else and C. Nayak , Phys. Rev. B 93 , 201103(R) ( 2016 ). PRBMDO 2469-9950 10.1103/PhysRevB.93.201103 [52] 52 A. C. Potter , T. Morimoto , and A. Vishwanath , Phys. Rev. X 6 , 041001 ( 2016 ). PRXHAE 2160-3308 10.1103/PhysRevX.6.041001 [53] 53 R. Roy and F. Harper , Phys. Rev. B 94 , 125105 ( 2016 ). PRBMDO 2469-9950 10.1103/PhysRevB.94.125105 [54] 54 S. Roy and G. J. Sreejith , Phys. Rev. B 94 , 214203 ( 2016 ). PRBMDO 2469-9950 10.1103/PhysRevB.94.214203 [55] 55 R. Roy and F. Harper , Phys. Rev. B 95 , 195128 ( 2017 ). PRBMDO 2469-9950 10.1103/PhysRevB.95.195128 [56] 56 H. C. Po , L. Fidkowski , T. Morimoto , A. C. Potter , and A. Vishwanath , Phys. Rev. X 6 , 041070 ( 2016 ). PRXHAE 2160-3308 10.1103/PhysRevX.6.041070 [57] 57 M. H. Kolodrubetz , F. Nathan , S. Gazit , T. Morimoto , and J. E. Moore , Phys. Rev. Lett. 120 , 150601 ( 2018 ). PRLTAO 0031-9007 10.1103/PhysRevLett.120.150601 [58] 58 T. Kinoshita , T. Wenger , and D. Weiss , Nature (London) 440 , 900 ( 2006 ). NATUAS 0028-0836 10.1038/nature04693 [59] 59 S. Hild , T. Fukuhara , P. Schauß , J. Zeiher , M. Knap , E. Demler , I. Bloch , and C. Gross , Phys. Rev. Lett. 113 , 147205 ( 2014 ). PRLTAO 0031-9007 10.1103/PhysRevLett.113.147205 [60] 60 M. Rigol , V. Dunjko , and M. Olshanii , Nature (London) 452 , 854 ( 2008 ). NATUAS 0028-0836 10.1038/nature06838 [61] 61 A. Lazarides , A. Das , and R. Moessner , Phys. Rev. E 90 , 012110 ( 2014 ). PRESCM 1539-3755 10.1103/PhysRevE.90.012110 [62] 62 A. Lazarides , A. Das , and R. Moessner , Phys. Rev. Lett. 112 , 150401 ( 2014 ). PRLTAO 0031-9007 10.1103/PhysRevLett.112.150401 [63] 63 V. Gritsev and A. Polkovnikov , SciPost Phys. 2 , 021 ( 2017 ). 2542-4653 10.21468/SciPostPhys.2.3.021 [64] 64 A. C. Cubero , SciPost Phys. 5 , 25 ( 2018 ). 2542-4653 10.21468/SciPostPhys.5.3.025 [65] 65 P. W. Claeys , S. De Baerdemacker , O. E. Araby , and J.-S. Caux , Phys. Rev. Lett. 121 , 080401 ( 2018 ). PRLTAO 0031-9007 10.1103/PhysRevLett.121.080401 [66] 66 M. Vanicat , L. Zadnik , and T. Prosen , Phys. Rev. Lett. 121 , 030606 ( 2018 ). PRLTAO 0031-9007 10.1103/PhysRevLett.121.030606 [67] 67 A. Bobenko , M. Bordemann , C. Gunn , and U. Pinkall , Commun. Math. Phys. 158 , 127 ( 1993 ). CMPHAY 0010-3616 10.1007/BF02097234 [68] 68 T. Prosen and C. Mejía-Monasterio , J. Phys. A 49 , 185003 ( 2016 ). JPAMB5 1751-8113 10.1088/1751-8113/49/18/185003 [69] 69 S. Gopalakrishnan , Phys. Rev. B 98 , 060302(R) ( 2018 ). PRBMDO 2469-9950 10.1103/PhysRevB.98.060302 [70] 70 T. Prosen and B. Buča , J. Phys. A 50 , 395002 ( 2017 ). JPAMB5 1751-8113 10.1088/1751-8121/aa85a3 [71] 71 S. Gopalakrishnan and B. Zakirov , Quantum Sci. Technol. 3 , 044004 ( 2018 ). 10.1088/2058-9565/aad759 [72] 72 S. Gopalakrishnan , D. A. Huse , V. Khemani , and R. Vasseur , Phys. Rev. B 98 , 220303(R) ( 2018 ). PRBMDO 2469-9950 10.1103/PhysRevB.98.220303 [73] 73 K. Klobas , M. Medenjak , T. Prosen , and M. Vanicat , arXiv:1807.05000 . [74] 74 B. Buča , J. P. Garrahan , T. Prosen , and M. Vanicat , Phys. Rev. E 100 , 020103 ( 2019 ). PRESCM 2470-0045 10.1103/PhysRevE.100.020103 [75] 75 V. Alba , J. Dubail , and M. Medenjak , Phys. Rev. Lett. 122 , 250603 ( 2019 ). PRLTAO 0031-9007 10.1103/PhysRevLett.122.250603 [76] 76 M. A. Nielsen and I. L. Chuang , Quantum Computation and Quantum Information: 10th Anniversary Edition , 10th ed. ( Cambridge University Press , New York, 2011 ). [77] 77 L. Vidmar and M. Rigol , J. Stat. Mech. ( 2016 ) 064007 . JSMTC6 1742-5468 10.1088/1742-5468/2016/06/064007 [78] 78 See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.123.170603 for a pedagogical derivation of the Coordinate and Thermodynamic Bethe Ansatz solutions of the dispersing FFA model, and brief derivations of hydrodynamics and operator spreading. [79] 79 C. N. Yang and C. P. Yang , J. Math. Phys. (N.Y.) 10 , 1115 ( 1969 ). JMAPAQ 0022-2488 10.1063/1.1664947 [80] 80 M. Takahashi , Thermodynamics of One-Dimensional Solvable Models ( Cambridge University Press , Cambridge, England, 1999 ). [81] 81 A. Zamolodchikov , Phys. Lett. B 253 , 391 ( 1991 ). PYLBAJ 0370-2693 10.1016/0370-2693(91)91737-G [82] 82 T. R. Klassen and E. Melzer , Nucl. Phys. B338 , 485 ( 1990 ). NUPBBO 0550-3213 10.1016/0550-3213(90)90643-R [83] 83 O. A. Castro-Alvaredo , B. Doyon , and T. Yoshimura , Phys. Rev. X 6 , 041065 ( 2016 ). PRXHAE 2160-3308 10.1103/PhysRevX.6.041065 [84] 84 B. Bertini , M. Collura , J. De Nardis , and M. Fagotti , Phys. Rev. Lett. 117 , 207201 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.117.207201 [85] 85 B. Doyon and T. Yoshimura , SciPost Phys. 2 , 014 ( 2017 ). 2542-4653 10.21468/SciPostPhys.2.2.014 [86] 86 B. Doyon and H. Spohn , SciPost Phys. 3 , 039 ( 2017 ). 2542-4653 10.21468/SciPostPhys.3.6.039 [87] 87 E. Ilievski and J. De Nardis , Phys. Rev. Lett. 119 , 020602 ( 2017 ). PRLTAO 0031-9007 10.1103/PhysRevLett.119.020602 [88] 88 V. B. Bulchandani , R. Vasseur , C. Karrasch , and J. E. Moore , Phys. Rev. B 97 , 045407 ( 2018 ). PRBMDO 2469-9950 10.1103/PhysRevB.97.045407 [89] 89 B. Doyon , T. Yoshimura , and J.-S. Caux , Phys. Rev. Lett. 120 , 045301 ( 2018 ). PRLTAO 0031-9007 10.1103/PhysRevLett.120.045301 [90] 90 L. Piroli , J. De Nardis , M. Collura , B. Bertini , and M. Fagotti , Phys. Rev. B 96 , 115124 ( 2017 ). PRBMDO 2469-9950 10.1103/PhysRevB.96.115124 [91] 91 E. Ilievski and J. De Nardis , Phys. Rev. B 96 , 081118(R) ( 2017 ). PRBMDO 2469-9950 10.1103/PhysRevB.96.081118 [92] 92 M. Collura , A. De Luca , and J. Viti , Phys. Rev. B 97 , 081111(R) ( 2018 ). PRBMDO 2469-9950 10.1103/PhysRevB.97.081111 [93] 93 V. Alba and P. Calabrese , Proc. Natl. Acad. Sci. U.S.A. 114 , 7947 ( 2017 ). PNASA6 0027-8424 10.1073/pnas.1703516114 [94] 94 A. De Luca , M. Collura , and J. De Nardis , Phys. Rev. B 96 , 020403(R) ( 2017 ). PRBMDO 2469-9950 10.1103/PhysRevB.96.020403 [95] 95 B. Bertini and L. Piroli , J. Stat. Mech. ( 2018 ) 033104 . JSMTC6 1742-5468 10.1088/1742-5468/aab04b [96] 96 V. B. Bulchandani , R. Vasseur , C. Karrasch , and J. E. Moore , Phys. Rev. Lett. 119 , 220604 ( 2017 ). PRLTAO 0031-9007 10.1103/PhysRevLett.119.220604 [97] 97 V. B. Bulchandani , J. Phys. A 50 , 435203 ( 2017 ). JPAMB5 1751-8113 10.1088/1751-8121/aa8c62 [98] 98 B. Doyon , J. Dubail , R. Konik , and T. Yoshimura , Phys. Rev. Lett. 119 , 195301 ( 2017 ). PRLTAO 0031-9007 10.1103/PhysRevLett.119.195301 [99] 99 J.-S. Caux , B. Doyon , J. Dubail , R. Konik , and T. Yoshimura , SciPost Phys. 6 , 070 ( 2019 ). 2542-4653 10.21468/SciPostPhys.6.6.070 [100] 100 X. Cao , V. B. Bulchandani , and J. E. Moore , Phys. Rev. Lett. 120 , 164101 ( 2018 ). PRLTAO 0031-9007 10.1103/PhysRevLett.120.164101 [101] 101 B. Doyon , SciPost Phys. 5 , 054 ( 2018 ). 2542-4653 10.21468/SciPostPhys.5.5.054 [102] 102 M. Schemmer , I. Bouchoule , B. Doyon , and J. Dubail , Phys. Rev. Lett. 122 , 090601 ( 2019 ). PRLTAO 0031-9007 10.1103/PhysRevLett.122.090601 [103] 103 J. De Nardis , D. Bernard , and B. Doyon , Phys. Rev. Lett. 121 , 160603 ( 2018 ). PRLTAO 0031-9007 10.1103/PhysRevLett.121.160603 [104] 104 L. Bonnes , F. H. L. Essler , and A. M. Läuchli , Phys. Rev. Lett. 113 , 187203 ( 2014 ). PRLTAO 0031-9007 10.1103/PhysRevLett.113.187203 [105] 105 A. Larkin and Y. N. Ovchinnikov , Sov. Phys. JETP 28 , 1200 ( 1969 ). SPHJAR 0038-5646 [106] 106 J. Maldacena , S. H. Shenker , and D. Stanford , J. High Energy Phys. 8 ( 2016 ) 106 . JHEPFG 1029-8479 10.1007/JHEP08(2016)106 [107] 107 C.-J. Lin and O. I. Motrunich , Phys. Rev. B 97 , 144304 ( 2018 ). PRBMDO 2469-9950 10.1103/PhysRevB.97.144304 [108] 108 V. Khemani , D. A. Huse , and A. Nahum , Phys. Rev. B 98 , 144304 ( 2018 ). PRBMDO 2469-9950 10.1103/PhysRevB.98.144304 [109] 109 M. Bruschi , P. Santini , and O. Ragnisco , Phys. Lett. A 169 , 151 ( 1992 ). PYLAAG 0375-9601 10.1016/0375-9601(92)90585-A [110] 110 B. Grammaticos , Y. Ohta , A. Ramani , D. Takahashi , and K. Tamizhmani , Phys. Lett. A 226 , 53 ( 1997 ). PYLAAG 0375-9601 10.1016/S0375-9601(96)00934-6 [111] 111 J. Preskill , Quantum 2 , 79 ( 2018 ). 10.22331/q-2018-08-06-79 [112] 112 K. X. Wei , P. Peng , O. Shtanko , I. Marvian , S. Lloyd , C. Ramanathan , and P. Cappellaro , Phys. Rev. Lett. 123 , 090605 ( 2019 ). PRLTAO 0031-9007 10.1103/PhysRevLett.123.090605 [113] 113 P. Roushan , C. Neill , J. Tangpanitanon , V. Bastidas , A. Megrant , R. Barends , Y. Chen , Z. Chen , B. Chiaro , A. Dunsworth , Science 358 , 1175 ( 2017 ). SCIEAS 0036-8075 10.1126/science.aao1401 Publisher Copyright: © 2019 American Physical Society.
PY - 2019/10/23
Y1 - 2019/10/23
N2 - We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write down and solve the Bethe equations for the generalized quantum model and show that these take on a particularly simple form that allows for an exact solution: Essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly, providing an exact description of interacting chiral particles in the thermodynamic limit. Although the model is interacting, its unusually simple structure allows us to construct operators that spread with no butterfly effect; this construction does not seem possible in other interacting integrable systems. This model exemplifies a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.
AB - We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write down and solve the Bethe equations for the generalized quantum model and show that these take on a particularly simple form that allows for an exact solution: Essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly, providing an exact description of interacting chiral particles in the thermodynamic limit. Although the model is interacting, its unusually simple structure allows us to construct operators that spread with no butterfly effect; this construction does not seem possible in other interacting integrable systems. This model exemplifies a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.
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U2 - 10.1103/PhysRevLett.123.170603
DO - 10.1103/PhysRevLett.123.170603
M3 - Article
C2 - 31702243
AN - SCOPUS:85074448344
SN - 0031-9007
VL - 123
JO - Physical review letters
JF - Physical review letters
IS - 17
M1 - 170603
ER -