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Hubbard model, conserved quantities, and computer algebra

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Abstract

The constants of motion of the half-filled four-point Hubbard model with cyclic boundary conditions are given in Wannier and Bloch representation. The total number operator and total spin operator are conserved and spin-reversal symmetry exists. In Wannier representation we have additionally the C4v symmetry and in Bloch representation we have the total momentum operator which is conserved. The anticommutation relations for Fermi operators with spin are implemented using computer algebra. Using computer algebra, all the constants of motion are given. The one-dimensional Hubbard model admits a Lax representation. From the Lax pair we find a new constant of motion.

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Authors and Affiliations

  1. Department of Applied Mathematics and Nonlinear Studies, Rand Afrikaans University, 2000, Johannesburg, South Africa

    W. -H. Steeb & C. M. Villet

  2. Institut für Angewandte Physik, Theoretische Quantunelektronik, Technische Hochschule Darmstadt, D-6100, Darmstadt, Germany

    P. Mulser

Authors
  1. W. -H. Steeb
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  2. C. M. Villet
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  3. P. Mulser
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Steeb, W.H., Villet, C.M. & Mulser, P. Hubbard model, conserved quantities, and computer algebra. Int J Theor Phys 32, 1445–1452 (1993). https://doi.org/10.1007/BF00675206

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  • DOI: https://doi.org/10.1007/BF00675206

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