Simulating heavy fermion physics in optical lattice: Periodic Anderson model with harmonic trapping potential

Abstract

The periodic Anderson model (PAM), where local electron orbitals interplay with itinerant electronic carriers, plays an essential role in our understanding of heavy fermion materials. Motivated by recent proposals for simulating the Kondo lattice model (KLM) in terms of alkaline-earth metal atoms, we take another step toward the simulation of PAM, which includes the crucial charge/valence fluctuation of local f-electrons beyond purely low-energy spin fluctuation in the KLM. To realize PAM, a transition induced by a suitable laser between the electronic excited and ground state of alkaline-earth metal atoms (¹S₀↔³P₀) is introduced. This leads to effective hybridization between local electrons and conduction electrons in PAM. Generally, the SU(N) version of PAM can be realized by our proposal, which gives a unique opportunity to detect large-N physics without complexity in realistic materials. In the present work, high-temperature physical features of standard [SU(2)] PAM with harmonic trapping potential are analyzed by quantum Monte Carlo and dynamic mean-field theory, where the Mott/orbital-selective Mott state was found to coexist with metallic states. Indications for near-future experiments are provided. We expect our theoretical proposal and (hopefully) forthcoming experiments will deepen our understanding of heavy fermion systems. At the same time, we hope these will trigger further studies on related Mott physics, quantum criticality, and non-trivial topology in both the inhomogeneous and nonequilibrium realms.

Keywords

optical lattice / heavy fermion / Mott transition

References

[1] A. C.Hewson, The Kondo Problem to Heavy Fermions, Cambridge University Press, 1993

[2] P.Coleman, Introduction to Many Body Physics, chapters 15 to 18, Cambridge University Press, 2015

[3] H.Tsunetsugu, M.Sigrist, and K.Ueda, The groundstate phase diagram of the one-dimensional Kondo lattice model,Rev. Mod. Phys.69(3), 809 (1997)

[4] H. V.Löhneysen, A.Rosch, M.Vojta, and P.Wölfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys.79(3), 1015(2007)

[5] C.Pfleiderer, Superconducting phases of f-electron compounds, Rev. Mod. Phys.81(4), 1551(2009)

[6] J. A.Mydoshand P. M.Oppeneer, Hidden order, superconductivity, and magnetism: The unsolved case of URu₂ Si₂, Rev. Mod. Phys.83(4), 1301(2011)

[7] Y. F.Yang, Two-fluid model for heavy electron physics, Rep. Prog. Phys.79(7), 074501(2016)

[8] S.Doniach, The Kondo lattice and weak antiferromagnetism, Physica B+C91, 231(1977)

[9] M.Vekić, J. W.Cannon, D. J.Scalapino, R. T.Scalettar, and R. L.Sugar, Competition between antiferromagnetic order and spin-liquid behavior in the twodimensional periodic Anderson model at half filling, Phys. Rev. Lett.74(12), 2367(1995)

[10] F. F.Assaad, Quantum Monte Carlo simulations of the half-filled two-dimensional Kondo lattice model, Phys. Rev. Lett.83(4), 796(1999)

[11] M.Köhl, H.Moritz, T.Stöferle, K.Günter, and T.Esslinger, Fermionic atoms in a three dimensional optical lattice: Observing Fermi surfaces, dynamics, and interactions, Phys. Rev. Lett.94(8), 080403(2005)

[12] R.Jördens, N.Strohmaier, K.Günter, H.Moritz, and T.Esslinger, A Mott insulator of fermionic atoms in an optical lattice, Nature455(7210), 204(2008)

[13] R. A.Hart, P. M.Duarte, T. L.Yang, X.Liu, T.Paiva, E.Khatami, R. T.Scalettar, N.Trivedi, D. A.Huse, and R. G.Hulet, Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms, Nature519(7542), 211(2015)

[14] D.Greif, M. F.Parsons, A.Mazurenko, C. S.Chiu, S.Blatt, F.Huber, G.Ji, and M.Greiner, Siteresolved imaging of a fermionic Mott insulator, Science351(6276), 953(2016)

[15] L. W.Cheuk, M. A.Nichols,K. R.Lawrence, M.Okan, H.Zhang, and M. W.Zwierlein, Observation of 2D fermionic Mott insulators of K⁴⁰ with single-site resolution, Phys. Rev. Lett.116(23), 235301(2016)

[16] M. F.Parsons, A.Mazurenko, C. S.Chiu, G.Ji, D.Greif, and M.Greiner, Site-resolved measurement of the spin-correlation function in the Hubbard model, Science353, 1253(2016)

[17] M.Boll, T. A.Hilker, G.Salomon, A.Omran, I.Bloch, and C.Gross, Spin and charge resolved quantum gas microscopy of antiferromagnetic order in Hubbard chains, Science353, 1257(2016)

[18] A. V.Gorshkov, M.Hermele, V.Gurarie, C.Xu, P. S.Julienne, J.Ye, P.Zoller, E.Demler, M. D.Lukin, and A. M.Rey, Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms, Nat. Phys.6(4), 289(2010)

[19] M.Foss-Feig, M.Hermele, and A. M.Rey, Probing the Kondo lattice model with alkaline-earth-metal atoms,Phys. Rev. A81, 051603(R) (2010)

[20] M.Foss-Feig, M.Hermele, V.Gurarie, and A. M.Rey, Heavy fermions in an optical lattice, Phys. Rev. A82(5), 053624(2010)

[21] J.Silva-Valenciaand A. M. C.Souza, Entanglement of alkaline-earth-metal fermionic atoms confined in optical lattices, Phys. Rev. A85(3), 033612(2012)

[22] J.Silva-Valenciaand A. M. C.Souza, Ground state of alkaline-earth fermionic atoms in one-dimensional optical lattices, Eur. Phys. J. B85, 5 (2012)

[23] B. N.Jiang, J.Qian, W. L.Wang, J.Du, andY. Z.Wang,Interacting heavy fermions in a disordered optical lattice,Eur. Phys. J. D68(12), 361(2014)

[24] L.Isaevand A. M.Rey, Heavy-fermion valence-bond liquids in ultracold atoms: Cooperation of the Kondo effect and geometric frustration, Phys. Rev. Lett.115(16), 165302(2015)

[25] L.Isaev, J.Schachenmayer, and A. M.Rey, Spin-Orbitcoupled correlated metal phase in Kondo lattices: An implementation with alkaline-earth atoms, Phys. Rev. Lett.117(13), 135302(2016)

[26] R.Zhang, D. P.Zhang, Y. T.Cheng, W.Chen, P.Zhang, and H.Zhai, Kondo effect in alkaline-earthmetal atomic gases with confinement-induced resonances, Phys. Rev. A93(4), 043601(2016)

[27] R.Zhang, Y. T.Cheng, H.Zhai, and P.Zhang, Orbital Feshbach resonance in alkali-earth atoms, Phys. Rev. Lett.115(13), 135301(2015)

[28] G.Pagano, M.Mancini, G.Cappellini, L.Livi, C.Sias, J.Catani, M.Inguscio, and L.Fallani, Strongly interacting gas of two-electron fermions at an orbital Feshbach resonance, Phys. Rev. Lett.115(26), 265301(2015)

[29] M.Höfer, L.Riegger, F.Scazza, C.Hofrichter, D. R.Fernandes, M. M.Parish, J.Levinsen, I.Bloch, and S.Fölling, Observation of an orbital interaction-induced Feshbach resonance in Yb¹⁷³, Phys. Rev. Lett.115(26), 265302(2015)

[30] M.Dzero, J.Xia, V.Galitski, and P.Coleman, Topological Kondo insulators, Annu. Rev. Condens. Matter Phys.7(1), 249(2016)

[31] H. Q.Yuan, F. M.Grosche, M.Deppe, C.Geibel, G.Sparn, and F.Steglich, Observation of two distinct superconducting phases in CeCu₂Si₂, Science302(5653), 2104(2003)

[32] J. P.Rueff, J. P.Itie, M.Taguchi, C. F.Hague, J. M.Mariot, R.Delaunay, J. P.Kappler, and N.Jaouen, Probing the γ–αtransition in bulk Ce under pressure: A Direct investigation by resonant inelastic X-ray scattering, Phys. Rev. Lett.96(23), 237403(2006)

[33] C.Pépin, Kondo breakdown as a selective Mott transition in the Anderson lattice, Phys. Rev. Lett.98(20), 206401(2007)

[34] Y.Zhong, K.Liu, Y. Q.Wang, and H. G.Luo, Alternative Kondo breakdown mechanism: Orbital-selective orthogonal metal transition, Phys. Rev. B86(11), 115113(2012)

[35] R.Blankenbecler, D. J.Scalapino, and R. L.Sugar, Monte Carlo calculations of coupled boson-fermion systems (I), Phys. Rev. D24(8), 2278(1981)

[36] J. E.Hirsch,Two-dimensional Hubbard model: Numerical simulation study,Phys. Rev. B31(7), 4403(1985)

[37] R. R.dos Santo, Braz. J. Phys.33, 1 (2003)

[38] A.Georges, G.Kotliar, W.Krauth, and M. J.Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys.68(1), 13(1996)

[39] M. M.Boyd, T.Zelevinsky, A. D.Ludlow, S.Blatt, T.Zanon-Willette, S. M.Foreman, and J.Ye, Nuclear spin effects in optical lattice clocks, Phys. Rev. A76(2), 022510(2007)

[40] G. K.Campbell, M. M.Boyd, J. W.Thomsen, M. J.Martin, S.Blatt, M. D.Swallows, T. L.Nicholson, T.Fortier, C. W.Oates, S. A.Diddams, N. D.Lemke, P.Naidon, P.Julienne, J.Ye, and A. D.Ludlow, Probing interactions between ultracold fermions, Science324(5925), 360(2009)

[41] M.Dzero, K.Sun, V.Galitski, and P.Coleman, Topological Kondo insulators, Phys. Rev. Lett.104(10), 106408(2010)

[42] T.Esslinger, Fermi–Hubbard physics with atoms in an optical lattice, Annu. Rev. Condens. Matter Phys.1(1), 129(2010)

[43] I.Bloch, J.Dalibard, and S.Nascimbene, Quantum simulations with ultracold quantum gases, Nat. Phys.8(4), 267(2012)

[44] Y.Zhong, K.Liu, Y. F.Wang, Y. Q.Wang, and H. G.Luo, Half-filled Kondo lattice on the honeycomb lattice, Eur. Phys. J. B86(5), 195(2013)

[45] L.De Leo, C.Kollath, A.Georges, M.Ferrero, and O.Parcollet, Trapping and cooling fermionic atoms into Mott and Néel states, Phys. Rev. Lett.101(21), 210403(2008)

[46] V. W.Scarola, L.Pollet, J.Oitmaa, and M.Troyer, Discerning incompressible and compressible phases of cold atoms in optical lattices, Phys. Rev. Lett.102(13), 135302(2009)

[47] S.Chiesa, C. N.Varney, M.Rigol, and R. T.Scalettar, Magnetism and pairing of two-dimensional trapped fermions, Phys. Rev. Lett.106(3), 035301(2011)

[48] T.Senthil, M.Vojta, andS.Sachdev, Weak magnetism and non-Fermi liquids near heavy-fermion critical points, Phys. Rev. B69(3), 035111(2004)

[49] M.Vojta, Orbital-selective Mott transitions: Heavy fermions and beyond, J. Low Temp. Phys.161(1–2), 203(2010)

[50] T.Paiva, R.Scalettar, M.Randeria, and N.Trivedi, Fermions in 2D optical lattices: Temperature and entropy scales for observing antiferromagnetism and superfluidity, Phys. Rev. Lett.104(6), 066406(2010)

[51] M.Jarrell, H.Akhlaghpour, and Th.Pruschke, Periodic Anderson model in infinite dimensions, Phys. Rev. Lett.70(11), 1670(1993)

[52] M. J.Rozenberg, G.Kotliar, and H.Kajueter,Transfer of spectral weight in spectroscopies of correlated electron systems, Phys. Rev. B54(12), 8452(1996)

[53] C. J.Wu, J. P.Hu, and S. C.Zhang, Exact SO(5) symmetry in the spin-3/2 fermionic system, Phys. Rev. Lett.91(18), 186402(2003)

[54] C. J.Wu, Exotic many-body physics with large-spin Fermi gases, Physics3, 92(2010)

[55] D.Wang, Y.Li, Z.Cai, Z. C.Zhou, Y.Wang, and C. J.Wu, Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning-field quantum Monte Carlo simulations, Phys. Rev. Lett.112(15), 156403(2014)

[56] Z. C.Zhou, D.Wang, Z. Y.Meng, Y.Wang, and C. J.Wu, Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions, Phys. Rev. B93(24), 245157(2016)

[57] S. M.Ramos, M. B.Fontes, E. N.Hering, M. A.Continentino, E.Baggio-Saitovich, F. D.Neto, E. M.Bittar, P. G.Pagliuso, E. D.Bauer, J. L.Sarrao, and J. D.Thompson, Superconducting quantum critical point in CeCoIn_5−xSn_x, Phys. Rev. Lett.105(12), 126401(2010)

[58] D. J.Scalapino, A common thread: The pairing interaction for unconventional superconductors, Rev. Mod. Phys.84(4), 1383(2012)

[59] P. W.Anderson, P. A.Lee, M.Randeria, T. M.Rice, N.Trivedi, and F. C.Zhang, The physics behind high-temperature superconducting cuprates: the plain vanilla version of RVB, J. Phys.: Condens. Matter16(24), R755(2004)

[60] P. A.Lee, N.Nagaosa, and X. G.Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys.78(1), 17(2006)

[61] Y.Zhong, L.Zhang, C.Shao, and H. G.Luo, Superfluid response in heavy fermion superconductors, Front. Phys.12(5), 127101(2017)

[62] M.Nakagawa and N.Kawakami, Laser-induced Kondo effect in ultracold alkaline-earth fermions, Phys. Rev. Lett.115(16), 165303 (2015)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg