Exact Solution of a Non-Hermitian Generalized Rabi Model
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Abstract
An integrable non-Hermitian generalized Rabi model is constructed. A twist matrix is introduced to the construction of Hamiltonian and generates the non-Hermitian properties. The Yang–Baxter integrability of the system is proven. The exact energy spectrum and eigenstates are obtained using the Bethe ansatz. The method given in this study provides a general way to construct integrable spin-boson models. -
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References
[1] Rabi I I 1937 Phys. Rev. 51 652 doi: 10.1103/PhysRev.51.652[2] Niemczyk T, Deppe F, Huebl H, Menzel E P, Hocke F, Schwarz M J, Garcia-Ripoll J J, Zueco D, Hümmer T, Solano E, Marx A, and Gross R 2010 Nat. Phys. 6 772 doi: 10.1038/nphys1730[3] Khitrova G, Gibbs H M, Kira M, Koch S W, and Scherer A 2006 Nat. Phys. 2 81 doi: 10.1038/nphys227[4] Leibfried D, Blatt R, Monroe C, and Wineland D 2003 Rev. Mod. Phys. 75 281 doi: 10.1103/RevModPhys.75.281[5] Dicke R H 1954 Phys. Rev. 93 99 doi: 10.1103/PhysRev.93.99[6] Flottat T, Hebert F, Rousseau V G, and Batrouni G G 2016 Eur. Phys. J. D 70 213 doi: 10.1140/epjd/e2016-70492-x[7] Schiro M, Bordyuh M, Oztop B, and Tureci H E 2013 J. Phys. B 46 224021 doi: 10.1088/0953-4075/46/22/224021[8] Lambert N, Emary C, and Brandes T 2004 Phys. Rev. Lett. 92 073602 doi: 10.1103/PhysRevLett.92.073602[9] Cui S, Cao J, Fan H, and Amico L 2017 J. Phys. A 50 204001 doi: 10.1088/1751-8121/aa6a6f[10] Lv X, Zhao C, and Zheng H 2017 J. Phys. A 50 074002 doi: 10.1088/1751-8121/aa5537[11] Xie Q 2020 Commun. Theor. Phys. 72 065105 doi: 10.1088/1572-9494/ab8a1f[12] Zhang Y, Mao B, Xu D, Zhang Y, You W, Liu M, and Luo H 2020 J. Phys. A 53 315302 doi: 10.1088/1751-8121/ab92be[13] Braak D 2011 Phys. Rev. Lett. 107 100401 doi: 10.1103/PhysRevLett.107.100401[14] Judd B R 1979 J. Phys. C 12 1685 doi: 10.1088/0022-3719/12/9/010[15] Xie Q, Cui S, Cao J, Amico L, and Fan H 2014 Phys. Rev. X 4 021046 doi: 10.1103/PhysRevX.4.021046[16] Skrypnyk T 2018 J. Phys. A 51 015204 doi: 10.1088/1751-8121/aa94af[17] Bogoliubov N M, Bulloughz R K, and Timonen J 1996 J. Phys. A 29 6305 doi: 10.1088/0305-4470/29/19/015[18] Bogoliubov N M 2000 J. Res. Natl. Bur. Stand. Sec. B 100 2051 doi: 10.1007/BF02675727[19] Rybin A, Kastelewiczz G, Timoneny J, and Bogoliubov N 1998 J. Phys. A 31 4705 doi: 10.1088/0305-4470/31/20/009[20] Amico L and Hikami K 2005 Eur. Phys. J. B 43 387 doi: 10.1140/epjb/e2005-00068-8[21] Kundu A 2007 SIGMA 3 040 doi: 10.3842/SIGMA.2007.040[22] Kundu A 2007 Theor. Math. Phys. 151 831 doi: 10.1007/s11232-007-0068-2[23] Amico L, Frahmb H, Osterlohb A, and Ribeiro G A P 2007 Nucl. Phys. B 787 283 doi: 10.1016/j.nuclphysb.2007.07.022[24] Dunning C, Isaac P S, Links J, and Zhao S 2011 Nucl. Phys. B 848 372 doi: 10.1016/j.nuclphysb.2011.03.001[25] Babelon O and Talalaev D 2007 J. Stat. Mech.: Theory Exp. 2007 P06013 doi: 10.1088/1742-5468/2007/06/P06013[26] Skrypnyk T 2008 J. Phys. A 41 475202 doi: 10.1088/1751-8113/41/47/475202[27] Skrypnyk T 2010 J. Phys. A 43 205205 doi: 10.1088/1751-8113/43/20/205205[28] Tschirhart H and Faribault A 2014 J. Phys. A 47 405204 doi: 10.1088/1751-8113/47/40/405204[29] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243 doi: 10.1103/PhysRevLett.80.5243[30] Rotter I 2009 J. Phys. A 42 153001 doi: 10.1088/1751-8113/42/15/153001[31] El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S, and Christodoulides D N 2018 Nat. Phys. 14 11 doi: 10.1038/nphys4323[32] Heiss W 2012 J. Phys. A 45 444016 doi: 10.1088/1751-8113/45/44/444016[33] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803 doi: 10.1103/PhysRevLett.121.086803[34] Okuma N, Kawabata K, Shiozaki K, and Sato M 2020 Phys. Rev. Lett. 124 086801 doi: 10.1103/PhysRevLett.124.086801[35] Zhang K, Yang Z, and Fang C 2020 Phys. Rev. Lett. 125 126402 doi: 10.1103/PhysRevLett.125.126402[36] Longhi S 2019 Phys. Rev. Lett. 122 237601 doi: 10.1103/PhysRevLett.122.237601[37] Longhi S 2021 Phys. Rev. B 103 054203 doi: 10.1103/PhysRevB.103.054203[38] Tzortzakakis A F, Makris K G, Szameit A, and Economou E N 2021 Phys. Rev. Res. 3 013208 doi: 10.1103/PhysRevResearch.3.013208 -
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