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Tomonaga-Luttinger Unusual Exponents around Fermi Points in the One-Dimensional Hubbard Model

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DOI: 10.4236/wjcmp.2015.52012    2,800 Downloads   3,198 Views   Citations

ABSTRACT

We study the correlation functions of one-dimensional Hubbard model in the presence of external magnetic field through the conformal field method. The long distance behaviour of the correlation functions and their unusual exponents for the model in the presence of a magnetic field are developed by solving the dressed charge matrix equations and setting the number of occupancies  to one, as alternative to the usual zero used by authors in literatures. This work shows that the exponent of the correlation functions is a monotonous function of magnetic field and the correlation functions decay as powers of these unusual exponents. As the magnetic field goes to zero, we obtain the exponents as 8.125, 11.125, 17.125, 26.125 and 38.125 at kF, 3kF, 5kF, 7kF and 9kF. Our analytical results will provide insights into criticality in condensed matter physics.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Nenuwe, N. and Idiodi, J. (2015) Tomonaga-Luttinger Unusual Exponents around Fermi Points in the One-Dimensional Hubbard Model. World Journal of Condensed Matter Physics, 5, 86-103. doi: 10.4236/wjcmp.2015.52012.

References

[1] Frahm, H. and Korepin, V.E. (1990) Critical Exponents for the One-Dimensional Hubbard Model. Physical Review B, 42, 10553-10565.
http://dx.doi.org/10.1103/PhysRevB.42.10553
[2] Lieb, E.H. and Wu, F.Y. (1968) Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension. Physical Review Letters, 20, 1445-1448.
http://dx.doi.org/10.1103/PhysRevLett.20.1445
[3] Woynarovich, F. (1989) Finite-Size Effects in a Non-Half-Filled Hubbard Chain. Journal of Physics A, 22, 4243-4256.
http://dx.doi.org/10.1088/0305-4470/22/19/017
[4] Nenuwe, O.N. and Akpojotor, F. (2015) Power-Law Dependence of Correlation Functions in the Tomonaga-Luttinger Liquid. International Journal of Theoretical and Mathematical Physics, 5, 8-15.
http://www.sapub.org/global/showpaperpdf.aspx?doi=10.5923/j.ijtmp.20150501.02
[5] Parola, A. and Sorella, S. (1990) Asymptotic Spin-Spin Correlations of the U→∞, One-Dimensional Hubbard Model. Physical Review Letters, 64, 1831-1834.
http://dx.doi.org/10.1103/PhysRevLett.64.1831
[6] Finkel’shtein, A.M. (1977) Correlation Functions in One-Dimensional Hubbard Model. JETP Letters, 25, 73-76.
[7] Luther, A. and Peschel, I. (1975) Calculation of Critical Exponents in Two Dimensions from Quantum Field Theory in one Dimension. Physical Review B, 12, 3906.
http://dx.doi.org/10.1103/physrevb.12.3908
[8] Belavin, A.A. Polyakov, A.M. and Zamolodchikov, A.B. (1984) Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory. Nuclear Physics B, 241, 333-380.
http://dx.doi.org/10.1016/0550-3213(84)90052-X
[9] Kawakami, N. and Yang, S.-K. (1991) Luttinger Liquid Properties of Highly Correlated Electron Systems in One Dimension. Journal of Physics: Condensed Matter, 3, 5983-6008.
http://dx.doi.org/10.1088/0953-8984/3/32/007
[10] Izergin, A.G., Korepin, V.E. and Reshetikhin, Y. (1989) Conformal Dimensions in Bethe Ansatz Solvable Models. Journal of Physics A, 22, 2615-2620.
http://dx.doi.org/10.1088/0305-4470/22/13/052
[11] Penc, K. and Solyom, J. (1993) One Dimensional Hubbard Model in a Magnetic Field and the Multicomponent Tomonaga-Luttinger Model. Physical Review B, 47, 6273-6292.
http://dx.doi.org/10.1103/PhysRevB.47.6273
[12] Fabian, H.L.E., Frahm, H., Frank, G.O.H., Andreas, K. and Korepin, V.E. (2005) The One-Dimensional Hubbard Model. Cambridge University Press, New York, 1-674.
[13] Yang, C.N. and Yang, C.P. (1966) One-Dimensional Chain of Anisotropic Spin-Spin Interactions. II. Properties of the Ground-State Energy per Lattice Site for an Infinite System. Physical Review Letters, 150, 327-339.
http://dx.doi.org/10.1103/PhysRev.150.327
[14] Kawakami, N. and Yang, S.-K. (1990) Luttinger Anomaly Exponent of Momentum Distribution in the Hubbard Chain. Physics Letters A, 148, 359-362.
http://dx.doi.org/10.1016/0375-9601(90)90818-9
[15] Qin, S.J. and Yu, L. (1996) Momentum Distribution Critical Exponents for the One-Dimensional Large-U Hubbard Model in the Thermodynamic Limit. Physical Review B, 54, 1447-1450.
http://dx.doi.org/10.1103/PhysRevB.54.1447
[16] Qin, S.J., Liang, S.D., Su, Z.B. and Yu, L. (1995) Density-Matrix Renormalization-Group Calculation of Correlation Functions in the One-Dimensional Hubbard Model. Physical Review B, 52, R5475-R5478.
http://dx.doi.org/10.1103/PhysRevB.52.R5475

  
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