Share This Article:

An Improved Finite Temperature Lanczos Method and Its Application to the Spin-1/2 Heisenberg Model on the Kagome Lattice

Abstract Full-Text HTML Download Download as PDF (Size:2792KB) PP. 134-140
DOI: 10.4236/wjcmp.2014.43018    2,061 Downloads   2,574 Views   Citations
Author(s)    Leave a comment

ABSTRACT

We present an improvement of the finite temperature Lanczos method in order to apply this method to systems at very low temperature. One proposal is to introduce two steps in this method. In the first step, we use the Chebyshev polynomial expansion to calculate exp(-H/T1) random vector> at moderate temperature T1. In the second step, we apply the ordinary finite temperature Lanczos method using the calculated state as the initial state of the Lanczos method. Another proposal is to employ a sampling method for selecting a random vector. By this sampling, we can improve an efficiency of calculations. Using the improved finite temperature Lanczos method, we calculate the specific heat of the spin-1/2 Heisenberg model on the kagome lattices of 27 and 30 sites.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Munehisa, T. (2014) An Improved Finite Temperature Lanczos Method and Its Application to the Spin-1/2 Heisenberg Model on the Kagome Lattice. World Journal of Condensed Matter Physics, 4, 134-140. doi: 10.4236/wjcmp.2014.43018.

References

[1] Zeng, C. and Elser, V. (1990) Numerical Studies of Antiferromagnetism on a Kagome Net. Physical Review B, 42, 8436-8444.
http://dx.doi.org/10.1103/PhysRevB.42.8436
[2] Elstner, N. and Young, A.P. (1994) Spin-1/2 Heisenberg Antiferromagnet on the Kagome Lattice: High-Temperature Expansion and Exact-Diagonalization Studies. Physical Review B, 50, 6871-6876.
http://dx.doi.org/10.1103/PhysRevB.50.6871
[3] Nakamura, T. and Miyashita, S. (1995) Thermodynamic Properties of the Quantum Heisenberg Antiferromagnet on the Kagome Lattice. Physical Review B, 52, 9174-9177.
http://dx.doi.org/10.1103/PhysRevB.52.9174
[4] Lecheminant, P., Bernu, B., Lhuillier, C., Pierre, L. and Sindzingre, P. (1997) Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagome Lattice Using Exact Spectra Analysis. Physical Review B, 56, 2521-2529.
http://dx.doi.org/10.1103/PhysRevB.56.2521
[5] Depenbrock, S., McCulloch, I.P. and Schollwoeck, U. (2012) Nature of the Spin-Liquid Ground State of the S = 1/2 Heisenberg Model on the Kagome Lattice. Physical Review Letter, 109, 067201-067201-6.
http://dx.doi.org/10.1103/PhysRevLett.109.067201
[6] Misguich, G., Serban, D. and Pasquier, V. (2002) Quantum Dimer Model on the Kagome Lattice: Solvable DimerLiquid and Ising Gauge Theory. Physical Review Letter, 89, 137202-137202-4.
http://dx.doi.org/10.1103/PhysRevLett.89.137202
[7] Hermele, M., Ran, Y., Lee, P.A. and Wen, X.G. (2008) Properties of an Algebraic Spin Liquid on the Kagome Lattice. Physical Review B, 77, 224413-224413-23.
http://dx.doi.org/10.1103/PhysRevB.77.224413
[8] Iqbal, Y., Becca, F., Sorella, S. and Poilblanc, D. (2013) Gapless Spin-Liquid Phase in the Kagome Spin-1/2 Heisenberg Antiferromagnet. Physical Review B, 87, 060405-060405-5.
http://dx.doi.org/10.1103/PhysRevB.87.060405
[9] Messio, L., Bernu, B. and Lhuillier, C. (2012) Kagome Antiferromagnet: A Chiral Topological Spin Liquid? Physical Review Letter, 108, 207204-207204-5.
http://dx.doi.org/10.1103/PhysRevLett.108.207204
[10] Clark, B.K., Kinder, J.M. Neuscamman, E., Chan, K.C. and Lawler, M.J. (2013) Striped Spin Liquid Crystal Ground State Instability of Kagome Antiferromagnets. Physical Review Letter, 111, 187205-87205-5.
[11] Fak, B., Kermarrec, E., Messio, L., Bernu, B., Lhuillier, C., Bert, F., Mendels, P., Koteswararao, B., Bouquet, F., Ollivier, J., Hillier, A.D., Amato, A., Colman, R.H. and Wills, A.S. (2012) Kapellasite: A Kagome Quantum Spin Liquid with Competing Interactions Experiments. Physical Review Letter, 109, 037208-037208-5.
http://dx.doi.org/10.1103/PhysRevLett.109.037208
[12] Misguich, G. and Bernu, B. (2005) Specific Heat of the S = 1/2 Heisenberg Model on the Kagome Lattice: HighTemperature Series Expansion Analysis. Physical Review B, 71, 014417-014417-7.
http://dx.doi.org/10.1103/PhysRevB.71.014417
[13] Misguich, G. and Sindzingre, P. (2007) Magnetic Susceptibility and Specific Heat of the Spin-1/2 Heisenberg Model on the Kagome Lattice and Experimental Data on ZnCu3(OH)6Cl2. The European Physical Journal B, 59, 305-309.
http://dx.doi.org/10.1140/epjb/e2007-00301-6
[14] Singh, R.R.P. and Oitmaa, J. (2012) High-Temperature Series Expansion Study of the Heisenberg Antiferromagnet on the Hyperkagome Lattice: Comparison with Na4Ir3O8. Physical Review B, 85, 104406-104406-4.
http://dx.doi.org/10.1103/PhysRevB.85.104406
[15] Laeuchli, A.M., Sudan, J. and Sorensen, E.S. (2011) Ground-State Energy and Spin Gap of Spin-12 Kagome-Heisenberg Antiferromagnetic Clusters: Large-Scale Exact Diagonalization Results. Physical Review B, 83, 212401-212404.
http://dx.doi.org/10.1103/PhysRevB.83.212401
[16] Nakano, H. and Sakai, T. (2011) Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet. Journal of the Physical Society of Japan, 80, 053704-053708.
http://dx.doi.org/10.1143/JPSJ.80.053704
[17] Isoda, M., Nakano, H. and Sakai, T. (2011) Specific Heat and Magnetic Susceptibility of Ising-Like Anisotropic Heisenberg Model on Kagome Lattice. Journal of the Physical Society of Japan, 80, 084704-084706.
http://dx.doi.org/10.1143/JPSJ.80.084704
[18] Weise, A., Wellein, G., Alvermann, A. and Fehske, H. (2006) The Kernel Polynomial Method. Review Modern Physics, 78, 275-306.
http://dx.doi.org/10.1103/RevModPhys.78.275
[19] Iitaka, T., Nomura, S., Hirayama, H., Zhao, X., Aoyagi, Y. and Sugano, T. (1997) Calculating the Linear Response Functions of Noninteracting Electrons with a Time-Dependent Schroedinger Equation. Physical Review E, 56, 12221229.
http://dx.doi.org/10.1103/PhysRevE.56.1222
[20] Jaklic, J. and Prelpvsek, P. (1994) Lanczos Method for the Calculation of Finite-Temperature Quantities in Correlated Systems. Physical Review B, 49, 5065-5068.
http://dx.doi.org/10.1103/PhysRevB.49.5065
[21] Jaklic, J. and Prelpvsek, P. (2000) Finite-Temperature Properties of Doped Antiferromagnets. Advance Physics, 49, 1-92.
http://dx.doi.org/10.1080/000187300243381
[22] Schnack, J. and Wendland, O. (2010) Properties of Highly Frustrated Magnetic Molecules Studied by the Finite-Temperature Lanczos Method. The European Physical Journal B, 78, 535-541.
http://dx.doi.org/10.1140/epjb/e2010-10713-8
[23] Long, M.W., Prelovsek, P., El Shawish, S., Karadamoglou, J. and Zotos, X. (2003) Finite-Temperature Dynamical Correlations Using the Microcanonical Ensemble and the Lanczos Algorithm. Physical Review B, 68, 235106-235106-10.
http://dx.doi.org/10.1103/PhysRevB.68.235106
[24] Capone, M., de’Medici, L. and Georges, A. (2007) Solving the Dynamical Mean-Field Theory at Very Low Temperatures Using the Lanczos Exact Diagonalization. Physical Review B, 76, 245116-245116-6.
http://dx.doi.org/10.1103/PhysRevB.76.245116
[25] Aichhorn, M., Daghofer, M., Evertz, H.G. and von der Linden, W. (2003) Low-Temperature Lanczos Method for Strongly Correlated Systems. Physical Review B, 67, 161103-161103-4.
http://dx.doi.org/10.1103/PhysRevB.67.161103
[26] Zerec, I., Schmidt, B. and Thalmeier, P. (2006) Kondo Lattice Model Studied with the Finite Temperature Lanczos Method. Physical Review B, 73, 245108-245108-6.
http://dx.doi.org/10.1103/PhysRevB.73.245108
[27] Schmidt, B., Thalmeier, P. and Shannon, N. (2007) Magnetocaloric Effect in the Frustrated Square Lattice J1-J2 Model. Physical Review B, 76, 125113-125113-19.
http://dx.doi.org/10.1103/PhysRevB.76.125113
[28] Hams, A. and De Raedt, H. (2000) Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices. Physical Review E, 62, 4365-4377.
http://dx.doi.org/10.1103/PhysRevE.62.4365
[29] Iitaka, T. and Ebisuzaki, T. (2004) Random Phase Vector for Calculating the Trace of a Large Matrix. Physical Review E, 69, 057701-057701-4.
http://dx.doi.org/10.1103/PhysRevE.69.057701

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.