Lieb’s Theorem and Maximum Entropy Condensates

Joseph Tindall1, Frank Schlawin2,3, Michael Sentef2, and Dieter Jaksch1,3,4

1Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
2Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
3The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, Hamburg, Germany
4Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany

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Abstract

Coherent driving has established itself as a powerful tool for guiding a many-body quantum system into a desirable, coherent non-equilibrium state. A thermodynamically large system will, however, almost always saturate to a featureless infinite temperature state under continuous driving and so the optical manipulation of many-body systems is considered feasible only if a transient, prethermal regime exists, where heating is suppressed. Here we show that, counterintuitively, in a broad class of lattices Floquet heating can actually be an advantageous effect. Specifically, we prove that the maximum entropy steady states which form upon driving the ground state of the Hubbard model on unbalanced bi-partite lattices possess uniform off-diagonal long-range order which remains finite even in the thermodynamic limit. This creation of a `hot' condensate can occur on $\textit{any}$ driven unbalanced lattice and provides an understanding of how heating can, at the macroscopic level, expose and alter the order in a quantum system. We discuss implications for recent experiments observing emergent superconductivity in photoexcited materials.

In general, heat is deleterious towards quantum effects. Under certain symmetry constraints, however, this is not true and heating can be used to re-arrange and expose order in a quantum system.
In this article we show how, in a paradigmatic electronic system, the amount of order which results from this process can be directly related to certain geometrical properties of the underlying lattice. This allows us to identify a range of lattice structures where heating can be used to manipulate and manifest quantum order even at the macroscopic level.
We discuss possible experimental realisations of our work and its potential as a novel method for engineering and controlling superconductivity.

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[1] C. J. Gazza, A. E. Trumper, and H. A. Ceccatto. The triangular-lattice Hubbard model: a frustrated highly correlated electron system. Journal of Physics: Condensed Matter, 6 (41): L625–L630, 1994. 10.1088/​0953-8984/​6/​41/​001.
https:/​/​doi.org/​10.1088/​0953-8984/​6/​41/​001

[2] W. Hofstetter and D. Vollhardt. Frustration of antiferromagnetism in the $t-t^{`}$-Hubbard model at weak coupling. Annalen der Physik, 510 (1): 48–55, 1998. 10.1002/​andp.19985100105.
https:/​/​doi.org/​10.1002/​andp.19985100105

[3] T. Ohashi, T. Momoi, H. Tsunetsugu, and N. Kawakami. Finite temperature Mott transition in Hubbard model on anisotropic triangular lattice. Phys. Rev. Lett., 100: 076402, 2008. 10.1103/​PhysRevLett.100.076402.
https:/​/​doi.org/​10.1103/​PhysRevLett.100.076402

[4] P. Sahebsara and D. Sénéchal. Hubbard model on the triangular lattice: Spiral order and spin liquid. Phys. Rev. Lett., 100: 136402, 2008. 10.1103/​PhysRevLett.100.136402.
https:/​/​doi.org/​10.1103/​PhysRevLett.100.136402

[5] H.-Y. Yang, A. M. Läuchli, F. Mila, and K. P. Schmidt. Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice. Phys. Rev. Lett., 105: 267204, 2010. 10.1103/​PhysRevLett.105.267204.
https:/​/​doi.org/​10.1103/​PhysRevLett.105.267204

[6] E. H. Lieb. Two theorems on the Hubbard model. Phys. Rev. Lett., 62: 1201–1204, 1989. 10.1103/​PhysRevLett.62.1201.
https:/​/​doi.org/​10.1103/​PhysRevLett.62.1201

[7] F. Šimkovic, J. P. F. LeBlanc, A. J. Kim, Y. Deng, N. V. Prokof'ev, B. V. Svistunov, and E. Kozik. Extended crossover from a Fermi liquid to a quasiantiferromagnet in the half-filled 2d Hubbard model. Phys. Rev. Lett., 124: 017003, 2020. 10.1103/​PhysRevLett.124.017003.
https:/​/​doi.org/​10.1103/​PhysRevLett.124.017003

[8] H. Tasaki. Hubbard model and the origin of ferromagnetism. The European Physical Journal B, 64 (3): 365–372, 2008. 10.1140/​epjb/​e2008-00113-2.
https:/​/​doi.org/​10.1140/​epjb/​e2008-00113-2

[9] H. Tasaki. From Nagaoka's Ferromagnetism to Flat-Band Ferromagnetism and Beyond: An Introduction to Ferromagnetism in the Hubbard Model. Progress of Theoretical Physics, 99 (4): 489–548, 1998. 10.1143/​PTP.99.489.
https:/​/​doi.org/​10.1143/​PTP.99.489

[10] N. C. Costa, T. Mendes-Santos, T. Paiva, R. R. dos Santos, and R. T. Scalettar. Ferromagnetism beyond Lieb's theorem. Phys. Rev. B, 94: 155107, 2016a. 10.1103/​PhysRevB.94.155107.
https:/​/​doi.org/​10.1103/​PhysRevB.94.155107

[11] T. Kaneko, T. Shirakawa, S. Sorella, and S. Yunoki. Photoinduced ${\eta}$ pairing in the Hubbard model. Phys. Rev. Lett., 122: 077002, 2019. 10.1103/​PhysRevLett.122.077002.
https:/​/​doi.org/​10.1103/​PhysRevLett.122.077002

[12] M. A. Sentef, A. Tokuno, A. Georges, and C. Kollath. Theory of laser-controlled competing superconducting and charge orders. Phys. Rev. Lett., 118: 087002, 2017. 10.1103/​PhysRevLett.118.087002.
https:/​/​doi.org/​10.1103/​PhysRevLett.118.087002

[13] M. A. Sentef, A. F. Kemper, A. Georges, and C. Kollath. Theory of light-enhanced phonon-mediated superconductivity. Phys. Rev. B, 93: 144506, 2016. 10.1103/​PhysRevB.93.144506.
https:/​/​doi.org/​10.1103/​PhysRevB.93.144506

[14] J. R. Coulthard, S. R. Clark, S. Al-Assam, A. Cavalleri, and D. Jaksch. Enhancement of superexchange pairing in the periodically driven Hubbard model. Phys. Rev. B, 96: 085104, 2017. 10.1103/​PhysRevB.96.085104.
https:/​/​doi.org/​10.1103/​PhysRevB.96.085104

[15] Matthew W. Cook and Stephen R. Clark. Controllable finite-momenta dynamical quasicondensation in the periodically driven one-dimensional Fermi-Hubbard model. Phys. Rev. A, 101: 033604, 2020. 10.1103/​PhysRevA.101.033604.
https:/​/​doi.org/​10.1103/​PhysRevA.101.033604

[16] R. Fujiuchi, T. Kaneko, K. Sugimoto, S. Yunoki, and Y. Ohta. Superconductivity and charge density wave under a time-dependent periodic field in the one-dimensional attractive Hubbard model. Phys. Rev. B, 101: 235122, 2020. 10.1103/​PhysRevB.101.235122.
https:/​/​doi.org/​10.1103/​PhysRevB.101.235122

[17] A. Chandran and S. L. Sondhi. Interaction-stabilized steady states in the driven $o(n)$ model. Phys. Rev. B, 93: 174305, 2016. 10.1103/​PhysRevB.93.174305.
https:/​/​doi.org/​10.1103/​PhysRevB.93.174305

[18] C. Rylands, E. B. Rozenbaum, V. Galitski, and R. Konik. Many-body dynamical localization in a kicked Lieb-Liniger gas. Phys. Rev. Lett., 124: 155302, 2020. 10.1103/​PhysRevLett.124.155302.
https:/​/​doi.org/​10.1103/​PhysRevLett.124.155302

[19] N. Tancogne-Dejean, M. A. Sentef, and A. Rubio. Ultrafast modification of Hubbard $u$ in a strongly correlated material: Ab initio high-harmonic generation in NiO. Phys. Rev. Lett., 121: 097402, 2018. 10.1103/​PhysRevLett.121.097402.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.097402

[20] T. Ishikawa, Y. Sagae, Y. Naitoh, Y. Kawakami, H. Itoh, K. Yamamoto, K. Yakushi, H. Kishida, T. Sasaki, S. Ishihara, Y. Tanaka, K. Yonemitsu, and S. Iwai. Optical freezing of charge motion in an organic conductor. Nature Communications, 5 (1): 5528, 2014. 10.1038/​ncomms6528.
https:/​/​doi.org/​10.1038/​ncomms6528

[21] S. Wall, D. Brida, S. R. Clark, H. P. Ehrke, D. Jaksch, A. Ardavan, S. Bonora, H. Uemura, Y. Takahashi, T. Hasegawa, H. Okamoto, G. Cerullo, and A. Cavalleri. Quantum interference between charge excitation paths in a solid-state Mott insulator. Nature Physics, 7 (2): 114–118, 2011. 10.1038/​nphys1831.
https:/​/​doi.org/​10.1038/​nphys1831

[22] C. Weeks and M. Franz. Topological insulators on the Lieb and perovskite lattices. Phys. Rev. B, 82: 085310, 2010. 10.1103/​PhysRevB.82.085310.
https:/​/​doi.org/​10.1103/​PhysRevB.82.085310

[23] E. H. da Silva Neto, B. Yu, M. Minola, R. Sutarto, E. Schierle, F. Boschini, M. Zonno, M. Bluschke, J. Higgins, Y. Li, G. Yu, E. Weschke, F. He, M. Le Tacon, R. L. Greene, M. Greven, G. A. Sawatzky, B. Keimer, and A. Damascelli. Doping-dependent charge order correlations in electron-doped cuprates. Science Advances, 2 (8), 2016. 10.1126/​sciadv.1600782.
https:/​/​doi.org/​10.1126/​sciadv.1600782

[24] N. Katayama, K. Kojima, T. Yamaguchi, S. Hattori, S. Tamura, K. Ohara, S. Kobayashi, K. Sugimoto, Y. Ohta, K. Saitoh, and H. Sawa. Slow dynamics of disordered zigzag chain molecules in layered LiVS$_{2}$ under electron irradiation. npj Quantum Materials, 6 (1): 16, 2021. 10.1038/​s41535-021-00313-w.
https:/​/​doi.org/​10.1038/​s41535-021-00313-w

[25] R. H. McKenzie. A strongly correlated electron model for the layered organic superconductors $\kappa$-(BEDT-TTF)$_{2}$X. arXiv e-prints, art. cond-mat/​9802198, 1998. URL https:/​/​arxiv.org/​abs/​cond-mat/​9802198.
https:/​/​arxiv.org/​abs/​cond-mat/​9802198

[26] M. R. Slot, T. S. Gardenier, P. H. Jacobse, G. C. P. van Miert, S. N. Kempkes, S. J. M. Zevenhuizen, C. M. Smith, D. Vanmaekelbergh, and I. Swart. Experimental realization and characterization of an electronic Lieb lattice. Nature Physics, 13 (7): 672–676, 2017. 10.1038/​nphys4105.
https:/​/​doi.org/​10.1038/​nphys4105

[27] R. Drost, T. Ojanen, A. Harju, and P. Liljeroth. Topological states in engineered atomic lattices. Nature Physics, 13 (7): 668–671, 2017. 10.1038/​nphys4080.
https:/​/​doi.org/​10.1038/​nphys4080

[28] L. Tapasztó, G. Dobrik, P. Lambin, and L. Biró. Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography. Nature Nanotechnology, 3 (7): 397–401, 2008. 10.1038/​nnano.2008.149.
https:/​/​doi.org/​10.1038/​nnano.2008.149

[29] M. Abel, S. Clair, O. Ourdjini, M. Mossoyan, and L. Porte. Single layer of polymeric Fe-Phthalocyanine: An organometallic sheet on metal and thin insulating film. Journal of the American Chemical Society, 133 (5): 1203–1205, 2011. 10.1021/​ja108628r.
https:/​/​doi.org/​10.1021/​ja108628r

[30] W. Jiang, S. Zhang, Z. Wang, F. Liu, and T. Low. Topological band engineering of Lieb lattice in Phthalocyanine-based metal–organic frameworks. Nano Letters, 20 (3): 1959–1966, 2020. 10.1021/​acs.nanolett.9b05242.
https:/​/​doi.org/​10.1021/​acs.nanolett.9b05242

[31] T. Kambe, R. Sakamoto, K. Hoshiko, K. Takada, J.-H. Miyachi, M.and Ryu, S. Sasaki, J. Kim, K. Nakazato, M. Takata, and H. Nishihara. $\pi$-conjugated Nickel Bis(dithiolene) complex nanosheet. Journal of the American Chemical Society, 135 (7): 2462–2465, 2013. 10.1021/​ja312380b.
https:/​/​doi.org/​10.1021/​ja312380b

[32] K. Otsubo and H. Kitagawa. Metal–organic framework thin films with well-controlled growth directions confirmed by x-ray study. APL Materials, 2 (12): 124105, 2014. 10.1063/​1.4899295.
https:/​/​doi.org/​10.1063/​1.4899295

[33] C. Wang, L. Chi, A. Ciesielski, and P. Samorì. Chemical synthesis at surfaces with atomic precision: Taming complexity and perfection. Angewandte Chemie International Edition, 58 (52): 18758–18775, 2019a. 10.1002/​anie.201906645.
https:/​/​doi.org/​10.1002/​anie.201906645

[34] L. Liu, Y. Sun, X. Cui, K. Qi, X. He, Q. Bao, W. Ma, J. Lu, H. Fang, P. Zhang, L. Zheng, L. Yu, D. J. Singh, Q. Xiong, L. Zhang, and W. Zheng. Bottom-up growth of homogeneous moiré superlattices in bismuth oxychloride spiral nanosheets. Nature Communications, 10 (1): 4472, 2019. 10.1038/​s41467-019-12347-7.
https:/​/​doi.org/​10.1038/​s41467-019-12347-7

[35] L. J. McGilly, A. Kerelsky, N. R. Finney, K. Shapovalov, E.-M. Shih, A. Ghiotto, Y. Zeng, S. L. Moore, W. Wu, Y. Bai, K. Watanabe, T. Taniguchi, M. Stengel, L. Zhou, J. Hone, X. Zhu, D. N. Basov, C. Dean, C. E. Dreyer, and A. N. Pasupathy. Visualization of moiré superlattices. Nature Nanotechnology, 15 (7): 580–584, 2020. 10.1038/​s41565-020-0708-3.
https:/​/​doi.org/​10.1038/​s41565-020-0708-3

[36] G. Abbas, Y. Li, H.e Wang, W.-X. Zhang, C. Wang, and H. Zhang. Recent advances in twisted structures of flatland materials and crafting moiré superlattices. Advanced Functional Materials, 30 (36): 2000878, 2020. 10.1002/​adfm.202000878.
https:/​/​doi.org/​10.1002/​adfm.202000878

[37] L. Wang, S. Zihlmann, M.-H. Liu, P. Makk, K. Watanabe, T. Taniguchi, A. Baumgartner, and C. Schönenberger. New generation of moiré superlattices in doubly aligned hBN/​graphene/​hBN heterostructures. Nano Letters, 19 (4): 2371–2376, 2019b. 10.1021/​acs.nanolett.8b05061.
https:/​/​doi.org/​10.1021/​acs.nanolett.8b05061

[38] D. M. Kennes, M. Claassen, L. Xian, A. Georges, A. J. Millis, J. Hone, C. R. Dean, D. N. Basov, A. N. Pasupathy, and A. Rubio. Moiré heterostructures as a condensed-matter quantum simulator. Nature Physics, 17 (2): 155–163, 2021. 10.1038/​s41567-020-01154-3.
https:/​/​doi.org/​10.1038/​s41567-020-01154-3

[39] L. Xian, M. Claassen, D. Kiese, M. M. Scherer, S. Trebst, D. M. Kennes, and A. Rubio. Realization of nearly dispersionless bands with strong orbital anisotropy from destructive interference in twisted bilayer Mo$\rm {S}_{2}$. Nature Communications, 12 (1): 5644, 2021. 10.1038/​s41467-021-25922-8.
https:/​/​doi.org/​10.1038/​s41467-021-25922-8

[40] Y. Tang, L. Li, T. Li, Y. Xu, S. Liu, K. Barmak, K. Watanabe, T. Taniguchi, A. H. MacDonald, J. Shan, and K. F. Mak. Simulation of Hubbard model physics in wse2/​ws2 moiré superlattices. Nature, 579 (7799): 353–358, 2020. 10.1038/​s41586-020-2085-3.
https:/​/​doi.org/​10.1038/​s41586-020-2085-3

[41] T. Esslinger. Fermi-Hubbard physics with atoms in an optical lattice. Annual Review of Condensed Matter Physics, 1 (1): 129–152, 2010. 10.1146/​annurev-conmatphys-070909-104059.
https:/​/​doi.org/​10.1146/​annurev-conmatphys-070909-104059

[42] M. Messer, K. Sandholzer, F. Görg, J. Minguzzi, R. Desbuquois, and T. Esslinger. Floquet dynamics in driven Fermi-Hubbard systems. Phys. Rev. Lett., 121: 233603, 2018. 10.1103/​PhysRevLett.121.233603.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.233603

[43] F. H. L. Essler, H. Frahm, F. Göhmann, A. Klümper, and V. E. Korepin. The One-Dimensional Hubbard Model. Cambridge University Press, 2005. 10.1017/​CBO9780511534843.
https:/​/​doi.org/​10.1017/​CBO9780511534843

[44] L. Campos Venuti, M. Cozzini, P. Buonsante, F. Massel, N. Bray-Ali, and P. Zanardi. Fidelity approach to the Hubbard model. Phys. Rev. B, 78: 115410, 2008. 10.1103/​PhysRevB.78.115410.
https:/​/​doi.org/​10.1103/​PhysRevB.78.115410

[45] T. Schäfer, F. Geles, D. Rost, G. Rohringer, E. Arrigoni, K. Held, N. Blümer, M. Aichhorn, and A. Toschi. Fate of the false Mott-Hubbard transition in two dimensions. Phys. Rev. B, 91: 125109, 2015. 10.1103/​PhysRevB.91.125109.
https:/​/​doi.org/​10.1103/​PhysRevB.91.125109

[46] J. P. F. LeBlanc and E. Gull. Equation of state of the fermionic two-dimensional Hubbard model. Phys. Rev. B, 88: 155108, 2013. 10.1103/​PhysRevB.88.155108.
https:/​/​doi.org/​10.1103/​PhysRevB.88.155108

[47] S.-Q. Shen, Z.-M. Qiu, and G.-S. Tian. Ferrimagnetic long-range order of the Hubbard model. Phys. Rev. Lett., 72: 1280–1282, 1994. 10.1103/​PhysRevLett.72.1280.
https:/​/​doi.org/​10.1103/​PhysRevLett.72.1280

[48] H. Yoshida and H. Katsura. Rigorous results on the ground state of the attractive $\mathrm{SU}(n)$ Hubbard model. Phys. Rev. Lett., 126: 100201, 2021. 10.1103/​PhysRevLett.126.100201.
https:/​/​doi.org/​10.1103/​PhysRevLett.126.100201

[49] S. R. White. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett., 69: 2863–2866, 1992. 10.1103/​PhysRevLett.69.2863.
https:/​/​doi.org/​10.1103/​PhysRevLett.69.2863

[50] B. Buca, J. Tindall, and D. Jaksch. Non-stationary coherent quantum many-body dynamics through dissipation. Nature Communications, 10 (1): 1730, 2019. 10.1038/​s41467-019-09757-y.
https:/​/​doi.org/​10.1038/​s41467-019-09757-y

[51] J. Tindall, B. Buča, J. R. Coulthard, and D. Jaksch. Heating-induced long-range ${\eta}$ pairing in the Hubbard model. Phys. Rev. Lett., 123: 030603, 2019. 10.1103/​PhysRevLett.123.030603.
https:/​/​doi.org/​10.1103/​PhysRevLett.123.030603

[52] J. Tindall, F. Schlawin, M. A. Sentef, and D. Jaksch. Analytical solution for the steady states of the driven Hubbard model. Phys. Rev. B, 103: 035146, 2021. 10.1103/​PhysRevB.103.035146.
https:/​/​doi.org/​10.1103/​PhysRevB.103.035146

[53] L. D'Alessio and M. Rigol. Long-time behavior of isolated periodically driven interacting lattice systems. Phys. Rev. X, 4: 041048, 2014. 10.1103/​PhysRevX.4.041048.
https:/​/​doi.org/​10.1103/​PhysRevX.4.041048

[54] P. Pedro, C. Anushya, Z. Papić, and Dmitry A. A. Periodically driven ergodic and many-body localized quantum systems. Annals of Physics, 353: 196–204, 2015. 10.1016/​j.aop.2014.11.008.
https:/​/​doi.org/​10.1016/​j.aop.2014.11.008

[55] C. Weeks and M. Franz. Flat bands with nontrivial topology in three dimensions. Phys. Rev. B, 85: 041104(R), 2012. 10.1103/​PhysRevB.85.041104.
https:/​/​doi.org/​10.1103/​PhysRevB.85.041104

[56] C. N. Yang. Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors. Rev. Mod. Phys., 34: 694–704, 1962. 10.1103/​RevModPhys.34.694.
https:/​/​doi.org/​10.1103/​RevModPhys.34.694

[57] G. L. Sewell. Off-diagonal long-range order and the Meissner effect. Journal of Statistical Physics, 61 (1): 415–422, 1990. 10.1007/​BF01013973.
https:/​/​doi.org/​10.1007/​BF01013973

[58] H. T. Nieh, G. Su, and B. H. Zhao. Off-diagonal long-range order: Meissner effect and flux quantization. Phys. Rev. B, 51: 3760–3764, 1995. 10.1103/​PhysRevB.51.3760.
https:/​/​doi.org/​10.1103/​PhysRevB.51.3760

[59] T. Leticia and S.-P. Laurent. Quantum simulation of the Hubbard model with ultracold fermions in optical lattices. Comptes Rendus Physique, 19 (6): 365–393, 2018. 10.1016/​j.crhy.2018.10.013. Quantum simulation /​ Simulation quantique.
https:/​/​doi.org/​10.1016/​j.crhy.2018.10.013

[60] M. Theis, G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J. Hecker Denschlag. Tuning the scattering length with an optically induced Feshbach resonance. Phys. Rev. Lett., 93, 2004. 10.1103/​PhysRevLett.93.123001.
https:/​/​doi.org/​10.1103/​PhysRevLett.93.123001

[61] S. Taie, H. Ozawa, T. Ichinose, T. Nishio, S. Nakajima, and Y. Takahashi. Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice. Science Advances, 1 (10), 2015. 10.1126/​sciadv.1500854.
https:/​/​doi.org/​10.1126/​sciadv.1500854

[62] H. Ozawa, S. Taie, T. Ichinose, and Y. Takahashi. Interaction-driven shift and distortion of a flat band in an optical Lieb lattice. Phys. Rev. Lett., 118: 175301, 2017. 10.1103/​PhysRevLett.118.175301.
https:/​/​doi.org/​10.1103/​PhysRevLett.118.175301

[63] M. Hyrkäs, V. Apaja, and M. Manninen. Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices. Phys. Rev. A, 87: 023614, 2013. 10.1103/​PhysRevA.87.023614.
https:/​/​doi.org/​10.1103/​PhysRevA.87.023614

[64] S. Flannigan, L. Madail, R. G. Dias, and A. Daley. Hubbard models and state preparation in an optical Lieb lattice. New Journal of Physics, 2021. 10.1088/​1367-2630/​abfd01.
https:/​/​doi.org/​10.1088/​1367-2630/​abfd01

[65] J. Tindall, F. Schlawin, M. Buzzi, D. Nicoletti, J. R. Coulthard, H. Gao, A. Cavalleri, M. A. Sentef, and D. Jaksch. Dynamical order and superconductivity in a frustrated many-body system. Phys. Rev. Lett., 125: 137001, 2020a. 10.1103/​PhysRevLett.125.137001.
https:/​/​doi.org/​10.1103/​PhysRevLett.125.137001

[66] F. Peronaci, M. Schiró, and O. Parcollet. Resonant thermalization of periodically driven strongly correlated electrons. Phys. Rev. Lett., 120: 197601, 2018. 10.1103/​PhysRevLett.120.197601.
https:/​/​doi.org/​10.1103/​PhysRevLett.120.197601

[67] Andreas H., Yuta M.i, Martin E., and Philipp W. Floquet prethermalization in the resonantly driven Hubbard model. EPL (Europhysics Letters), 120 (5): 57001, 2017. 10.1209/​0295-5075/​120/​57001.
https:/​/​doi.org/​10.1209/​0295-5075/​120/​57001

[68] A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner. A cold-atom Fermi–Hubbard antiferromagnet. Nature, 545 (7655): 462–466, 2017. 10.1038/​nature22362.
https:/​/​doi.org/​10.1038/​nature22362

[69] A. Kantian, A. J. Daley, and P. Zoller. ${\eta}$ condensate of Fermionic atom pairs via adiabatic state preparation. Phys. Rev. Lett., 104: 240406, 2010. 10.1103/​PhysRevLett.104.240406.
https:/​/​doi.org/​10.1103/​PhysRevLett.104.240406

[70] G. D. Mahan. Many-Particle Physics. Springer, New York, 1981. 10.1007/​978-1-4757-5714-9.
https:/​/​doi.org/​10.1007/​978-1-4757-5714-9

[71] R. Anderson, F. Wang, P. Xu, V. Venu, S. Trotzky, F. Chevy, and J. H. Thywissen. Conductivity spectrum of ultracold atoms in an optical lattice. Phys. Rev. Lett., 122: 153602, 2019. 10.1103/​PhysRevLett.122.153602.
https:/​/​doi.org/​10.1103/​PhysRevLett.122.153602

[72] W. Zhigang, T. Edward, and Z. Eugene. Probing the optical conductivity of trapped charge-neutral quantum gases. EPL (Europhysics Letters), 110 (2): 26002, 2015. 10.1209/​0295-5075/​110/​26002.
https:/​/​doi.org/​10.1209/​0295-5075/​110/​26002

[73] A. Tokuno and T. Giamarchi. Spectroscopy for cold atom gases in periodically phase-modulated optical lattices. Phys. Rev. Lett., 106: 205301, 2011. 10.1103/​PhysRevLett.106.205301.
https:/​/​doi.org/​10.1103/​PhysRevLett.106.205301

[74] N. C. Costa, T. Mendes-Santos, T. Paiva, R. R. dos Santos, and R. T. Scalettar. Ferromagnetism beyond Lieb's theorem. Phys. Rev. B, 94: 155107, 2016b. 10.1103/​PhysRevB.94.155107.
https:/​/​doi.org/​10.1103/​PhysRevB.94.155107

[75] J. Tindall, F. Schlawin, M. Buzzi, D. Nicoletti, J. R. Coulthard, H. Gao, A. Cavalleri, M. A. Sentef, and D. Jaksch. Dynamical order and superconductivity in a frustrated many-body system. Phys. Rev. Lett., 125: 137001, 2020b. 10.1103/​PhysRevLett.125.137001.
https:/​/​doi.org/​10.1103/​PhysRevLett.125.137001

[76] M. Buzzi, D. Nicoletti, M. Fechner, N. Tancogne-Dejean, M. A. Sentef, A. Georges, T. Biesner, E. Uykur, M. Dressel, A. Henderson, T. Siegrist, J. A. Schlueter, K. Miyagawa, K. Kanoda, M.-S. Nam, A. Ardavan, J. Coulthard, J. Tindall, F. Schlawin, D. Jaksch, and A. Cavalleri. Photomolecular high-temperature superconductivity. Phys. Rev. X, 10: 031028, 2020. 10.1103/​PhysRevX.10.031028.
https:/​/​doi.org/​10.1103/​PhysRevX.10.031028

[77] M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri. Possible light-induced superconductivity in K$_3$C$_{60}$ at high temperature. Nature, 530 (7591): 461—464, 2016. 10.1038/​nature16522.
https:/​/​doi.org/​10.1038/​nature16522

[78] W. Hu, S. Kaiser, D. Nicoletti, C. R. Hunt, I. Gierz, M. C. Hoffmann, M. Le Tacon, T. Loew, B. Keimer, and A. Cavalleri. Optically enhanced coherent transport in YBa$_{2}$Cu$_{3}$O$_{6.5}$ by ultrafast redistribution of interlayer coupling. Nature Materials, 13 (7): 705–711, 2014. 10.1038/​nmat3963.
https:/​/​doi.org/​10.1038/​nmat3963

[79] D. Nicoletti, E. Casandruc, Y. Laplace, V. Khanna, C. R. Hunt, S. Kaiser, S. S. Dhesi, G. D. Gu, J. P. Hill, and A. Cavalleri. Optically induced superconductivity in striped La$_{2-x}$Ba$_{x}$CuO$_{4}$ by polarization-selective excitation in the near infrared. Phys. Rev. B, 90: 100503(R), 2014. 10.1103/​PhysRevB.90.100503.
https:/​/​doi.org/​10.1103/​PhysRevB.90.100503

[80] M. Budden, T. Gebert, M. Buzzi, G. Jotzu, E. Wang, T. Matsuyama, G. Meier, Y. Laplace, D. Pontiroli, M. Riccò, F. Schlawin, D. Jaksch, and A. Cavalleri. Evidence for metastable photo-induced superconductivity in k3c60. Nature Physics, 17 (5): 611–618, 2021. 10.1038/​s41567-020-01148-1.
https:/​/​doi.org/​10.1038/​s41567-020-01148-1

[81] A. Julku, S. Peotta, T. I. Vanhala, D.-H. Kim, and P. Törmä. Geometric origin of superfluidity in the Lieb-lattice flat band. Phys. Rev. Lett., 117: 045303, 2016. 10.1103/​PhysRevLett.117.045303.
https:/​/​doi.org/​10.1103/​PhysRevLett.117.045303

[82] A. Cavalleri. Photo-induced superconductivity. Contemporary Physics, 59 (1): 31–46, 2018. 10.1080/​00107514.2017.1406623.
https:/​/​doi.org/​10.1080/​00107514.2017.1406623

Cited by

[1] Joseph Tindall, Amy Searle, Abdulla Alhajri, and Dieter Jaksch, "Quantum physics in connected worlds", Nature Communications 13 1, 7445 (2022).

[2] Y. B. Shi, K. L. Zhang, and Z. Song, "Dynamic generation of nonequilibrium superconducting states in a Kitaev chain", Physical Review B 106 18, 184505 (2022).

[3] A. M. Marques, J. Mögerle, G. Pelegrí, S. Flannigan, R. G. Dias, and A. J. Daley, "Kaleidoscopes of Hofstadter butterflies and Aharonov-Bohm caging from 2n -root topology in decorated square lattices", Physical Review Research 5 2, 023110 (2023).

[4] A. M. Marques and R. G. Dias, "Generalized Lieb's theorem for noninteracting non-Hermitian n -partite tight-binding lattices", Physical Review B 106 20, 205146 (2022).

[5] Masaya Nakagawa, Naoto Tsuji, Norio Kawakami, and Masahito Ueda, "$\eta$ Pairing of Light-Emitting Fermions: Nonequilibrium Pairing Mechanism at High Temperatures", arXiv:2103.13624, (2021).

The above citations are from Crossref's cited-by service (last updated successfully 2023-12-06 21:59:45) and SAO/NASA ADS (last updated successfully 2023-12-06 21:59:46). The list may be incomplete as not all publishers provide suitable and complete citation data.