Some Exact Results in the One-Dimensional Attractive Hubbard Model

• Authors: D. Jakubczyk
• Languages of publication: EN

Abstracts

EN

The one-dimensional attractive Hubbard model (Ułl 0) is discussed for the chains of N nodes and the same number of electrons, where N-1 of them have the same spin projection, assuming periodic boundary conditions and the half-filling case. Based on the analysis of the eigenvalue problem we provided the general analytical expression for the eigenvalues, for any number N. This formula implies the existence of two elementary particles with mutually dependent momenta on the ring with N sites the same number of electrons including N-1 of the same spin projection.

Keywords

EN

75.10.Pq; 03.65.Aa; 03.65.Fd

Discipline

• 75.10.Pq: Spin chain models
• 03.65.Aa: Quantum systems with finite Hilbert space
• 03.65.Fd: Algebraic methods(see also 02.20.-a Group theory)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2015
• Volume: 128
• Issue: 2
• Pages: 170-172

Dates

published

2015-08

Contributors

author

D. Jakubczyk

• Department of Physics, Rzeszów University of Technology, al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland

References

• [1] J. Hubbard, Proc. R. Soc. A 276, 238 (1963), doi: 10.1098/rspa.1963.0204
• [2] M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963), doi: 10.1103/PhysRevLett.10.159
• [3] M.C. Gutzwiller, Phys. Rev. A 137, 1726 (1965), doi: 10.1103/PhysRev.137.A1726
• [4] M. Vojta, Rep. Prog. Phys. 66, 2069 (2003), doi: 10.1088/0034-4885/66/12/R01
• [5] The Theory of Superconductivity in the High-$T_c$ Cuprates, Eds. P.W. Anderson, S.B. Treiman, Princeton Series in Physics, Princeton Univ. Press 1997
• [6] M. Aizenman, E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason, Phys. Rev. A 70, 023612 (2004), doi: 10.1103/PhysRevA.70.023612
• [7] K. Kucab, G. Górski, J. Mizia, Physica C 490, 10 (2013), doi: 10.1016/j.physc.2013.04.016
• [8] E.H. Lieb, F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968), doi: 10.1103/PhysRevLett.20.1445
• [9] C.N. Yang, Phys. Rev. Lett. 19, 1315 (1967), doi: 10.1103/PhysRevLett.19.1312
• [10] F.H.L. Essler, V.E. Korepin, K. Schoutens, Phys. Rev. Lett. 67, 3848 (1991), doi: 10.1103/PhysRevLett.67.3848
• [11] T. Lulek, B. Lulek, D. Jakubczyk, P. Jakubczyk, Physica B: Condens. Matter 382, 162 (2006), doi: 10.1016/j.physb.2006.02.015
• [12] J. Milewski, B. Lulek, T. Lulek, Phys. Status Solidi B 244, 2497 (2007), doi: 10.1002/pssb.200674634
• [13] D. Jakubczyk, Acta Phys. Pol. B 44, 1921 (2013), doi: 10.5506/APhysPolB.44.1921
• [14] D. Jakubczyk, Acta Phys. Pol. B 45, 1759 (2014), doi: 10.5506/APhysPolB.45.1759
• [15] D. Jerome, C.R. Pasquier, Frontiers in Superconducting Materials, Ed. A.V. Narlikar, Springer, Berlin 2005
• [16] S.R.J.F. Clark, Strongly Correlated One-Dimensional Systems of Cold Atoms in Optical Lattices, Trinity College, Oxford 2007
• [17] D. Jakubczyk, Mod. Phys. Lett. B 26, 1150005 (2012), doi: 10.1142/S0217984911500059
• [18] B. Lulek, T. Lulek, A. Wal, P. Jakubczyk, Physica B 337, 375 (2003), doi: 10.1142/S0217984911500059
• [19] F.H.L. Essler, H. Frahm, F. Göhmann, A. Klümper, V.E. Korepin, The One-Dimensional Hubbard Model, Cambridge University Press, Cambridge 2005
• [20] A.B. Eriksson, T. Einarsson, S. Ostlund, Phys. Rev. B 52, 3662 (1995), doi: 10.1103/PhysRevB.52.3662

Identifiers

DOI

10.12693/APhysPolA.128.170