Tan relations in one dimension. (English) Zbl 1227.82090
Summary: We derive exact relations that connect the universal \(C/k^4\)-decay of the momentum distribution at large \(k\) with both thermodynamic properties and correlation functions of two-component Fermi gases in one dimension with contact interactions. The relations are analogous to those obtained by Tan in the three-dimensional case and are derived from an operator product expansion of the one- and two-particle density matrix. They extend earlier results by M. Olshanii and V. Dunjko [Phys. Rev. Lett. 91, 090401 (2003)] for the bosonic Lieb-Liniger gas. As an application, we calculate the pair distribution function at short distances and the dimensionless contact in the limit of infinite repulsion. The ground state energy approaches a universal constant in this limit, a behavior that also holds in the three-dimensional case. In both one and three dimensions, a Stoner instability to a saturated ferromagnet for repulsive fermions with zero range interactions is ruled out at any finite coupling.
References:
| [1] | Lieb, E. H.; Mattis, D. C., Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles (1966), Academic Press |
| [2] | Sutherland, B., Beautiful Models (2004), World Scientific Publishing |
| [3] | Giamarchi, T., Quantum Physics in One Dimension (2004), Oxford Science Publications · Zbl 1075.81001 |
| [4] | Tan, S., Annals of Physics, 323, 2952-2970 (2008) · Zbl 1159.82015 |
| [5] | E. Braaten, 2010, arXiv:1008.2922; E. Braaten, 2010, arXiv:1008.2922 |
| [6] | Tan, S., Annals of Physics, 323, 2971-2986 (2008) · Zbl 1160.82001 |
| [7] | Braaten, E.; Platter, L., Phys. Rev. Lett., 100, 205301 (2008) |
| [8] | Gaudin, M., Physics Letters A, 24, 55-56 (1967) |
| [9] | Yang, C. N., Phys. Rev. Lett., 19, 1312-1315 (1967) · Zbl 0152.46301 |
| [10] | Batchelor, M. T.; Bortz, M.; Guan, X. W.; Oelkers, N., J. Phys. A: Math. Gen., 39, 1073-1098 (2006) · Zbl 1330.82019 |
| [11] | Bloch, I.; Dalibard, J.; Zwerger, W., Rev. Mod. Phys., 80, 885-964 (2008) |
| [12] | Ketterle, W.; Zwierlein, M., Ultracold fermi gases, (Inguscio, M.; Ketterle, W.; Salomon, C., Proceedings of the International School of Physics Enrico Fermi, Varenna (2008), IOS Press: IOS Press Amsterdam) |
| [13] | Giorgini, S.; Pitaevskii, L. P.; Stringari, S., Rev. Mod. Phys., 80, 1215-1274 (2008) |
| [14] | Son, D. T.; Wingate, M., Annals of Physics, 321, 197-224 (2006) · Zbl 1107.82419 |
| [15] | Nishida, Y.; Son, D. T., Phys. Rev. D, 76, 086004 (2007) |
| [16] | Abrikosov, A. A.; Gorkov, L. P.; Dzyaloshinski, I. E., Methods of quantum field theory in statistical physics (1963), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0135.45003 |
| [17] | Duine, R. A.; MacDonald, A. H., Phys. Rev. Lett., 95, 230403 (2005) |
| [18] | Jo, G.-B.; Lee, Y.-R.; Choi, J.-H.; Christensen, C. A.; Kim, T. H.; Thywissen, J. H.; Pritchard, D. E.; Ketterle, W., Science, 325, 1521-1524 (2009) |
| [19] | Cui, X.; Zhai, H., Phys. Rev. A, 81, 041602 (2010) |
| [20] | Pilati, S.; Bertaina, G.; Giorgini, S.; Troyer, M., Phys. Rev. Lett., 105, 030405 (2010) |
| [21] | Chang, S.-Y.; Randeria, M.; Trivedi, N., Proc. Nat. Acad. Sci., 108, 51-54 (2011) |
| [22] | Wilson, K. G., Phys. Rev., 179, 1499-1512 (1969) |
| [23] | Kadanoff, L. P., Phys. Rev. Lett., 23, 1430-1433 (1969) |
| [24] | Olshanii, M.; Dunjko, V., Phys. Rev. Lett., 91, 090401 (2003) |
| [25] | Lieb, E. H.; Liniger, W., Phys. Rev., 130, 1605-1616 (1963) · Zbl 0138.23001 |
| [26] | Olshanii, M., Phys. Rev. Lett., 81, 938-941 (1998) |
| [27] | Braaten, E.; Kang, D.; Platter, L., Phys. Rev. A, 78, 053606 (2008) |
| [28] | Thomas, J. E.; Kinast, J.; Turlapov, A., Phys. Rev. Lett., 95, 120402 (2005) |
| [29] | Tan, S., Annals of Physics, 323, 2987-2990 (2008) · Zbl 1157.82382 |
| [30] | Fuchs, J. N.; Recati, A.; Zwerger, W., Phys. Rev. Lett., 93, 090408 (2004) |
| [31] | Tokatly, I. V., Phys. Rev. Lett., 93, 090405 (2004) |
| [32] | Hu, H.; Liu, X.-J.; Drummond, P. D., Europhysics Letters, 91, 20005 (2010) |
| [33] | Haldane, F. D.M., Phys. Rev. Lett., 47, 1840-1843 (1981) |
| [34] | Luther, A.; Emery, V. J., Phys. Rev. Lett., 33, 589-592 (1974) |
| [35] | Batchelor, M. T.; Bortz, M.; Guan, X. W.; Oelkers, N., Journal of Physics: Conference Series, 42, 5-10 (2006) · Zbl 1330.82019 |
| [36] | Krivnov, V. Y.; Ovchinnikov, A. A., Sov. Phys. -JETP, 40, 781 (1975) |
| [37] | Gangardt, D. M.; Shlyapnikov, G. V., Phys. Rev. Lett., 90, 010401 (2003) |
| [38] | Lieb, E.; Mattis, D., Phys. Rev., 125, 164-172 (1962) · Zbl 0118.46202 |
| [39] | Aizenman, M.; Lieb, E. H., Phys. Rev. Lett., 65, 1470-1473 (1990) |
| [40] | Strack, R.; Vollhardt, D., Phys. Rev. Lett., 72, 3425-3428 (1994) |
| [41] | Kollar, M.; Strack, R.; Vollhardt, D., Phys. Rev. B, 53, 9225-9231 (1996) |
| [42] | Girardeau, M., Journal of Mathematical Physics, 1, 516-523 (1960) · Zbl 0098.21704 |
| [43] | Zwerger, W., Science, 325, 1507-1509 (2009) |
| [44] | Pekker, D.; Babadi, M.; Sensarma, R.; Zinner, N.; Pollet, L.; Zwierlein, M. W.; Demler, E., Phys. Rev. Lett., 106, 050402 (2011) |
| [45] | T.-L.H. Shizhong Zhang, 2011, arXiv:1102.5687v1; T.-L.H. Shizhong Zhang, 2011, arXiv:1102.5687v1 |
| [46] | Sommer, A.; Ku, M.; Roati, G.; Zwierlein, M. W., Nature, 472, 201-204 (2011) |
| [47] | Cowell, S.; Heiselberg, H.; Mazets, I. E.; Morales, J.; Pandharipande, V. R.; Pethick, C. J., Phys. Rev. Lett., 88, 210403 (2002) |
| [48] | Song, J. L.; Zhou, F., Phys. Rev. Lett., 103, 025302 (2009) |
| [49] | Liu, X.-J.; Hu, H.; Drummond, P. D., Phys. Rev. A, 82, 023619 (2010) |
| [50] | Vollhardt, D., Rev. Mod. Phys., 56, 99 (1984) |
| [51] | Ainsworth, T. L.; Bedell, K. S.; Brown, G. E.; Quader, K. F., J. Low Temp. Phys., 50, 319-336 (1983) |
| [52] | Kanamori, J., Prog. Theor. Phys., 30, 275-289 (1963) · Zbl 0151.46703 |
| [53] | Gebhard, F., The Mott Metal-Insulator Transition, (Springer Tracts in Modern Physics, vol. 137 (1997), Springer: Springer Berlin, Heidelberg) |
| [54] | Nagaoka, Y., Phys. Rev., 147, 392-405 (1966) |
| [55] | Hanisch, T.; Uhrig, G. S.; Müller-Hartmann, E., Phys. Rev. B, 56, 13960-13982 (1997) |
| [56] | Zhang, S.; Leggett, A. J., Phys. Rev. A, 79, 023601 (2009) |
| [57] | Kohn, W.; Luttinger, J. M., Phys. Rev. Lett., 15, 524-526 (1965) |
| [58] | Moritz, H.; Stöferle, T.; Günter, K.; Köhl, M.; Esslinger, T., Phys. Rev. Lett., 94, 210401 (2005) |
| [59] | Schmidt, R.; Enss, T., Phys. Rev. A, 83, 6, 063620 (2011) |
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.
