×

What is an integrable quench? (English) Zbl 1375.81191

Summary: Inspired by classical results in integrable boundary quantum field theory, we propose a definition of integrable initial states for quantum quenches in lattice models. They are defined as the states which are annihilated by all local conserved charges that are odd under space reflection. We show that this class includes the states which can be related to integrable boundary conditions in an appropriate rotated channel, in loose analogy with the picture in quantum field theory. Furthermore, we provide an efficient method to test integrability of given initial states. We revisit the recent literature of global quenches in several models and show that, in all of the cases where closed-form analytical results could be obtained, the initial state is integrable according to our definition. In the prototypical example of the XXZ spin-\(s\) chains we show that integrable states include two-site product states but also larger families of matrix product states with arbitrary bond dimension. We argue that our results could be practically useful for the study of quantum quenches in generic integrable models.

MSC:

81T25 Quantum field theory on lattices
81R12 Groups and algebras in quantum theory and relations with integrable systems
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Baxter, R. J., Exactly Solvable Models in Statistical Mechanics (1982), Academic Press · Zbl 0538.60093
[2] Korepin, V. E.; Bogoliubov, N. M.; Izergin, A. G., Quantum Inverse Scattering Method and Correlation Functions (1993), Cambridge University Press · Zbl 0787.47006
[3] Jimbo, M.; Miwa, T., Algebraic Analysis of Solvable Lattice Models (1995), American Math. Soc.: American Math. Soc. Providence, RI · Zbl 0828.17018
[4] Takahashi, M., Thermodynamics of One-Dimensional Solvable Models (1999), Cambridge University Press · Zbl 1046.82007
[5] Essler, F. H.L.; Frahm, H.; Göhmann, F.; Klümper, A.; Korepin, V. E., The One-Dimensional Hubbard Model (2005), Cambridge University Press · Zbl 1107.82014
[6] Jimbo, M.; Miwa, T., Phys. Rev. D, 24, 3169 (1981)
[7] Slavnov, N. A., Theor. Math. Phys., 82, 273 (1990)
[8] Jimbo, M.; Miwa, T., J. Phys. A, Math. Gen., 29, 2923 (1996) · Zbl 0896.35114
[9] Kitanine, N.; Maillet, J. M.; Terras, V., Nucl. Phys. B, 554, 647 (1999) · Zbl 0972.82014
[10] Kitanine, N.; Maillet, J. M.; Slavnov, N. A.; Terras, V., Nucl. Phys. B, 641, 487 (2002) · Zbl 0998.82008
[11] Boos, H. E.; Göhmann, F.; Klümper, A.; Suzuki, J., J. Phys. A, Math. Theor., 40, Article 10699 pp. (2007) · Zbl 1147.82316
[12] Caux, J.-S.; Hagemans, R.; Maillet, J. M., J. Stat. Mech., Article P09003 pp. (2005)
[13] Jimbo, M.; Miwa, T.; Smirnov, F., J. Phys. A, Math. Theor., 42, Article 304018 pp. (2009) · Zbl 1179.82030
[14] Aufgebauer, B.; Klümper, A., J. Phys. A, Math. Theor., 45, Article 345203 pp. (2012) · Zbl 1252.82022
[15] Panfil, M.; Caux, J.-S., Phys. Rev. A, 89, Article 33605 pp. (2014)
[16] Piroli, L.; Calabrese, P., Phys. Rev. A, 94, Article 53620 pp. (2016)
[17] Calabrese, P.; Cardy, J., J. Stat. Mech., Article P06008 pp. (2007) · Zbl 1456.81358
[18] Delfino, G.; Viti, J., J. Phys. A, Math. Theor., 50, Article 84004 pp. (2017) · Zbl 1361.82023
[19] Bloch, I.; Dalibard, J.; Zwerger, W., Rev. Mod. Phys., 80, 885 (2008)
[20] Cazalilla, M. A.; Citro, R.; Giamarchi, T.; Orignac, E.; Rigol, M., Rev. Mod. Phys., 83, 1405 (2011)
[21] Polkovnikov, A.; Sengupta, K.; Silva, A.; Vengalattore, M., Rev. Mod. Phys., 83, 863 (2011)
[22] Langen, T.; Gasenzer, T.; Schmiedmayer, J., J. Stat. Mech., Article 64009 pp. (2016) · Zbl 1456.81242
[23] Calabrese, P.; Essler, F. H.L.; Mussardo, G., J. Stat. Mech., Article 64001 pp. (2016)
[24] Faribault, A.; Calabrese, P.; Caux, J.-S., J. Stat. Mech., Article P03018 pp. (2009)
[25] Mossel, J.; Palacios, G.; Caux, J.-S., J. Stat. Mech., Article L09001 pp. (2010)
[26] Kozlowski, K. K.; Pozsgay, B., J. Stat. Mech., Article P05021 pp. (2012) · Zbl 1456.82283
[27] Pozsgay, B., J. Stat. Mech., Article P06011 pp. (2014)
[28] Brockmann, M.; De Nardis, J.; Wouters, B.; Caux, J.-S., J. Phys. A, Math. Theor., 47, Article 145003 pp. (2014) · Zbl 1290.82003
[29] De Nardis, J.; Wouters, B.; Brockmann, M.; Caux, J.-S., Phys. Rev. A, 89, Article 33601 pp. (2014) · Zbl 1290.82003
[30] Korepin, V. E., Commun. Math. Phys., 86, 391 (1982) · Zbl 0531.60096
[31] Sotiriadis, S.; Takács, G.; Mussardo, G., Phys. Lett. B, 734, 52 (2014)
[32] Piroli, L.; Calabrese, P., J. Phys. A, Math. Theor., 47, Article 385003 pp. (2014) · Zbl 1302.82028
[33] Brockmann, M.; De Nardis, J.; Wouters, B.; Caux, J.-S., J. Phys. A, Math. Theor., 47, Article 345003 pp. (2014) · Zbl 1290.82003
[34] Brockmann, M., J. Stat. Mech., Article P05006 pp. (2014)
[35] de Leeuw, M.; Kristjansen, C.; Zarembo, K., J. High Energy Phys., 8, Article 98 pp. (2015) · Zbl 1388.81228
[36] Bucciantini, L., J. Stat. Phys., 164, 621 (2016) · Zbl 1348.82052
[37] Mazza, P. P.; Stéphan, J.-M.; Canovi, E.; Alba, V.; Brockmann, M.; Haque, M., J. Stat. Mech., Article 13104 pp. (2016) · Zbl 1456.81465
[38] Horváth, D. X.; Sotiriadis, S.; Takács, G., Nucl. Phys. B, 902, 508 (2016) · Zbl 1332.81120
[39] Buhl-Mortensen, I.; de Leeuw, M.; Kristjansen, C.; Zarembo, K., J. High Energy Phys., 2, Article 52 pp. (2016) · Zbl 1388.81499
[40] Foda, O.; Zarembo, K., J. Stat. Mech., Article 23107 pp. (2016) · Zbl 1456.82259
[41] de Leeuw, M.; Kristjansen, C.; Mori, S., Phys. Lett. B, 763, 197 (2016) · Zbl 1370.81150
[42] Horváth, D. X.; Takács, G., Phys. Lett. B, 771, 539 (2017) · Zbl 1372.81109
[43] Brockmann, M.; Stéphan, J.-M., J. Phys. A, Math. Theor., 50, Article 354001 pp. (2017) · Zbl 1376.82015
[44] Caux, J.-S.; Essler, F. H.L., Phys. Rev. Lett., 110, Article 257203 pp. (2013)
[45] Caux, J.-S., J. Stat. Mech., Article 64006 pp. (2016) · Zbl 1456.81227
[46] Brockmann, M.; Wouters, B.; Fioretto, D.; De Nardis, J.; Vlijm, R.; Caux, J.-S., J. Stat. Mech., Article P12009 pp. (2014)
[47] Mestyán, M.; Pozsgay, B.; Takács, G.; Werner, M. A., J. Stat. Mech., Article P04001 pp. (2015) · Zbl 1456.82298
[48] Bertini, B.; Schuricht, D.; Essler, F. H.L., J. Stat. Mech., Article P10035 pp. (2014)
[49] De Nardis, J.; Caux, J.-S., J. Stat. Mech., Article P12012 pp. (2014)
[50] De Luca, A.; Martelloni, G.; Viti, J., Phys. Rev. A, 91, Article 21603 pp. (2015)
[51] De Nardis, J.; Piroli, L.; Caux, J.-S., J. Phys. A, Math. Theor., 48, Article 43FT01 pp. (2015) · Zbl 1330.82041
[52] Bertini, B.; Piroli, L.; Calabrese, P., J. Stat. Mech., Article 63102 pp. (2016) · Zbl 1456.81226
[53] Piroli, L.; Calabrese, P.; Essler, F. H.L., SciPost Phys., 1, 1 (2016)
[54] Alba, V.; Calabrese, P., J. Stat. Mech., Article 43105 pp. (2016) · Zbl 1456.82215
[55] Mestyán, M.; Bertini, B.; Piroli, L.; Calabrese, P., J. Stat. Mech., Article 083103 pp. (2017) · Zbl 1457.82214
[56] Piroli, L.; Calabrese, P., Phys. Rev. A, 96, Article 023611 pp. (2017)
[57] Alba, V.; Calabrese, P.
[58] Bertini, B.; Tartaglia, E.; Calabrese, P. (2017)
[59] Pozsgay, B., J. Stat. Mech., Article P10028 pp. (2013)
[60] Piroli, L.; Pozsgay, B.; Vernier, E., J. Stat. Mech., Article 23106 pp. (2017)
[61] Calabrese, P.; Cardy, J., J. Stat. Mech., Article P10004 pp. (2007)
[62] Calabrese, P.; Cardy, J., J. Stat. Mech., Article 64003 pp. (2016) · Zbl 1456.81359
[63] Cardy, J., J. Stat. Mech., Article 023103 pp. (2016)
[64] Cardy, J., SciPost Phys., 3, Article 011 pp. (2017)
[65] Ghoshal, S.; Zamolodchikov, A., Int. J. Mod. Phys. A, 9, 3841 (1994)
[66] Ghoshal, S., Int. J. Mod. Phys. A, 9, 4801 (1994)
[67] Fioretto, D.; Mussardo, G., New J. Phys., 12, Article 55015 pp. (2010) · Zbl 1375.81169
[68] Sotiriadis, S.; Fioretto, D.; Mussardo, G., J. Stat. Mech., Article P02017 pp. (2012)
[69] Pálmai, T.; Sotiriadis, S., Phys. Rev. E, 90, Article 52102 pp. (2014)
[70] Allegra, N.; Dubail, J.; Stéphan, J.-M.; Viti, J., J. Stat. Mech., Article 053108 pp. (2016) · Zbl 1456.82220
[71] Collura, M.; De Luca, A.; Viti, J. (2017)
[72] Ilievski, E.; Quinn, E.; De Nardis, J.; Brockmann, M., J. Stat. Mech., Article 63101 pp. (2016) · Zbl 1456.82050
[73] Ilievski, E.; Medenjak, M.; Prosen, T.; Zadnik, L., J. Stat. Mech., Article 64008 pp. (2016) · Zbl 1456.81238
[74] Prosen, T., Nucl. Phys. B, 886, 1177 (2014) · Zbl 1325.82015
[75] Pereira, R. G.; Pasquier, V.; Sirker, J.; Affleck, I., J. Stat. Mech., Article P09037 pp. (2014) · Zbl 1456.82171
[76] Prosen, T.; Ilievski, E., Phys. Rev. Lett., 111, Article 057203 pp. (2013)
[77] Ilievski, E.; Medenjak, M.; Prosen, T., Phys. Rev. Lett., 115, Article 120601 pp. (2015)
[78] Fagotti, M., J. Stat. Mech., Article P03016 pp. (2014)
[79] Piroli, L.; Vernier, E., J. Stat. Mech., Article 53106 pp. (2016) · Zbl 1456.82307
[80] De Luca, A.; Collura, M.; De Nardis, J., Phys. Rev. B, 96, Article 020403 pp. (2017)
[81] Fagotti, M., J. Phys. A, Math. Theor., 50, Article 34005 pp. (2017) · Zbl 1357.82037
[82] Vernier, E.; Cortés Cubero, A., J. Stat. Mech., Article 23101 pp. (2017) · Zbl 1456.81449
[83] Rigol, M.; Dunjko, V.; Yurovsky, V.; Olshanii, M., Phys. Rev. Lett., 98, Article 050405 pp. (2007)
[84] Vidmar, L.; Rigol, M., J. Stat. Mech., Article 064007 pp. (2016) · Zbl 1456.81118
[85] Essler, F. H.L.; Fagotti, M., J. Stat. Mech., Article 064002 pp. (2016) · Zbl 1456.82585
[86] Fagotti, M.; Essler, F. H.L., J. Stat. Mech., Article P07012 pp. (2013)
[87] Pozsgay, B., J. Stat. Mech., Article P07003 pp. (2013)
[88] Mussardo, G., Phys. Rev. Lett., 111, Article 100401 pp. (2013)
[89] Fagotti, M.; Collura, M.; Essler, F. H.L.; Calabrese, P., Phys. Rev. B, 89, Article 125101 pp. (2014)
[90] Pozsgay, B., J. Stat. Mech., Article P09026 pp. (2014)
[91] Goldstein, G.; Andrei, N., Phys. Rev. A, 90, Article 43625 pp. (2014)
[92] Ilievski, E.; De Nardis, J.; Wouters, B.; Caux, J.-S.; Essler, F. H.L.; Prosen, T., Phys. Rev. Lett., 115, Article 157201 pp. (2015)
[93] Essler, F. H.L.; Mussardo, G.; Panfil, M., Phys. Rev. A, 91, Article 51602 pp. (2015)
[94] Piroli, L.; Vernier, E.; Calabrese, P., Phys. Rev. B, 94, Article 54313 pp. (2016)
[95] Essler, F. H.L.; Mussardo, G.; Panfil, M., J. Stat. Mech., Article 13103 pp. (2017) · Zbl 1457.82064
[96] Ilievski, E.; Quinn, E.; Caux, J.-S., Phys. Rev. B, 95, Article 115128 pp. (2017)
[97] Pozsgay, B.; Vernier, E.; Werner, M. A. (2017)
[98] Delfino, G., J. Phys. A, Math. Gen., 37, R45 (2004) · Zbl 1119.81383
[99] Cardy, J. L., Nucl. Phys. B, 324, 581 (1989)
[100] Zamolodchikov, A. B., Int. J. Mod. Phys. A, 4, 4235 (1989)
[101] Grabowski, M. P.; Mathieu, P., J. Phys. A, Math. Gen., 29, 7635 (1996) · Zbl 0906.60083
[102] Fagotti, M., J. Stat. Mech., Article 63105 pp. (2016)
[103] Faddeev, L. D.
[104] Grabowski, M. P.; Mathieu, P., Ann. Phys., 243, 299 (1995) · Zbl 0834.35105
[105] Perez-Garcia, D.; Verstraete, F.; Wolf, M. M.; Cirac, J. I., Quantum Inf. Comput., 7, 401 (2007) · Zbl 1152.81795
[106] Verstraete, F.; Cirac, J. I., Phys. Rev. B, 73, Article 94423 pp. (2006)
[107] Vidal, G., Phys. Rev. Lett., 91, Article 147902 pp. (2003)
[108] Pozsgay, B., J. Stat. Mech., Article P01011 pp. (2011)
[109] Rieger, H.; Iglói, F., Phys. Rev. B, 84, Article 165117 pp. (2011)
[110] Schuricht, D.; Essler, F. H.L., J. Stat. Mech., Article P04017 pp. (2012)
[111] Evangelisti, S., J. Stat. Mech., Article P04003 pp. (2013)
[112] Moca, C. P.; Kormos, M.; Zaránd, G., Phys. Rev. Lett., 119, Article 100603 pp. (2017)
[113] Cortés Cubero, A.; Schuricht, D. (2017)
[114] Piroli, L.; Vernier, E.; Calabrese, P.; Rigol, M., Phys. Rev. B, 95, Article 054308 pp. (2017)
[115] Rezek, Y.; Kosloff, R., New J. Phys., 8, 83 (2006)
[116] Fagotti, M.; Calabrese, P., Phys. Rev. A, 78, Article 010306 pp. (2008)
[117] Polkovnikov, A., Ann. Phys., 326, 486 (2011) · Zbl 1211.82023
[118] Santos, L. F.; Polkovnikov, A.; Rigol, M., Phys. Rev. Lett., 107, Article 040601 pp. (2011)
[119] Gurarie, V., J. Stat. Mech., Article P02014 pp. (2013)
[120] Collura, M.; Kormos, M.; Calabrese, P., J. Stat. Mech., Article P01009 pp. (2014)
[121] Schuricht, D., J. Stat. Mech., Article P11004 pp. (2015)
[122] Mukhin, E.; Tarasov, V.; Varchenko, A., Commun. Math. Phys., 288, 1 (2009) · Zbl 1173.82006
[123] Klümper, A., Z. Phys. B, Condens. Matter, 91, 507 (1993)
[124] Klümper, A., Lect. Notes Phys., 645, 349 (2004)
[125] Gómez, C.; Ruiz-Altaba, M.; Sierra, G., Quantum Groups in Two-Dimensional Physics (1996), Cambridge University Press · Zbl 0885.17011
[126] Kulish, P. P.; Reshetikhin, N. Y.; Sklyanin, E. K., Lett. Math. Phys., 5, 393 (1981) · Zbl 0502.35074
[127] Suzuki, J., J. Phys. A, Math. Gen., 32, 2341 (1999) · Zbl 0964.82015
[128] Barmettler, P.; Punk, M.; Gritsev, V.; Demler, E.; Altman, E., Phys. Rev. Lett., 102, Article 130603 pp. (2009)
[129] Barmettler, P.; Punk, M.; Gritsev, V.; Demler, E.; Altman, E., New J. Phys., 12, Article 55017 pp. (2010)
[130] Mossel, J.; Caux, J.-S., New J. Phys., 12, Article 55028 pp. (2010)
[131] Liu, W.; Andrei, N., Phys. Rev. Lett., 112, Article 257204 pp. (2014)
[132] Alba, V.; Calabrese, P., Proc. Natl. Acad. Sci. USA, 114, 7947 (2017) · Zbl 1404.82033
[133] Fagotti, M.; Essler, F. H.L., Phys. Rev. B, 87, Article 245107 pp. (2013)
[134] Pozsgay, B., J. Stat. Mech., Article P10045 pp. (2014)
[135] Pozsgay, B.; Eisler, V., J. Stat. Mech., Article 53107 pp. (2016)
[136] Zamolodchikov, A. B.; Fateev, V. A., Sov. J. Nucl. Phys., 32, 298 (1980)
[137] Inami, T.; Odake, S.; Zhang, Y.-Z., Nucl. Phys. B, 470, 419 (1996) · Zbl 1003.82508
[138] Zhou, Y., Nucl. Phys. B, 458, 504 (1996) · Zbl 1003.82506
[139] Sutherland, B., Phys. Rev. B, 12, 3795 (1975)
[140] Arnaudon, D.; Avan, J.; Crampé, N.; Doikou, A.; Frappat, L.; Ragoucy, E., J. Stat. Mech., Article P08005 pp. (2004)
[141] Doikou, A.; Nepomechie, R. I., Nucl. Phys. B, 521, 547 (1998) · Zbl 1047.82512
[142] Kuniba, A.; Nakanishi, T.; Suzuki, J., J. Phys. A, Math. Theor., 44, Article 103001 pp. (2011) · Zbl 1222.82041
[143] Zamolodchikov, A. B., Phys. Lett. B, 253, 391 (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.