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Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation

Received: 8 November 2022     Accepted: 9 January 2023     Published: 24 February 2023
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Abstract

It is pointed out that the low energy effective theory of a generalized spin system relates to the more generalized system shown by the Hubbard-like model. When the onsite repulsion is assumed to be provided by hard-core repulsion, a generalized fermion with flavour and colour degrees of freedom is used to define the Hubbard-like Hamiltonian in this case. In the strong coupling limit and at half filling this reduces to an antiferromagnet. The D-theory then helps us to associate the continuum limit of the (4+1)D aniferromagnet to 4D principal chiral model. It has been observed that in the strong coupling limit the problem of finding the ground state of lattice QCD is identical to that of solving the generalized antiferromagnet with Neel order playing the role of chiral symmetry breaking. In view of this, now formulate the Hubbard-like model Hamiltonian in terms of the gener- alized fermions with flavor and color degrees of freedom also shall consider the D-theoretical framework to show that the antiferromagnetic system which arises in the strong coupling limit and at half filling corresponds to the principal chiral model in the continuum limit with dimensional reduction. Also pointed out that at strong coupling and half filling the system reduces to a Heisenberg antiferromagnet. This result is analogous to the result obtained in standard Hubbard model.

Published in International Journal of High Energy Physics (Volume 10, Issue 1)
DOI 10.11648/j.ijhep.20231001.11
Page(s) 1-6
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2023. Published by Science Publishing Group

Keywords

Hubbard Model, Antiferromagnet, D- Framework, Chiral Breaking

References
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  • APA Style

    Subhamoy Singha Roy. (2023). Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation. International Journal of High Energy Physics, 10(1), 1-6. https://doi.org/10.11648/j.ijhep.20231001.11

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    ACS Style

    Subhamoy Singha Roy. Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation. Int. J. High Energy Phys. 2023, 10(1), 1-6. doi: 10.11648/j.ijhep.20231001.11

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    AMA Style

    Subhamoy Singha Roy. Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation. Int J High Energy Phys. 2023;10(1):1-6. doi: 10.11648/j.ijhep.20231001.11

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  • @article{10.11648/j.ijhep.20231001.11,
      author = {Subhamoy Singha Roy},
      title = {Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation},
      journal = {International Journal of High Energy Physics},
      volume = {10},
      number = {1},
      pages = {1-6},
      doi = {10.11648/j.ijhep.20231001.11},
      url = {https://doi.org/10.11648/j.ijhep.20231001.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20231001.11},
      abstract = {It is pointed out that the low energy effective theory of a generalized spin system relates to the more generalized system shown by the Hubbard-like model. When the onsite repulsion is assumed to be provided by hard-core repulsion, a generalized fermion with flavour and colour degrees of freedom is used to define the Hubbard-like Hamiltonian in this case. In the strong coupling limit and at half filling this reduces to an antiferromagnet. The D-theory then helps us to associate the continuum limit of the (4+1)D aniferromagnet to 4D principal chiral model. It has been observed that in the strong coupling limit the problem of finding the ground state of lattice QCD is identical to that of solving the generalized antiferromagnet with Neel order playing the role of chiral symmetry breaking. In view of this, now formulate the Hubbard-like model Hamiltonian in terms of the gener- alized fermions with flavor and color degrees of freedom also shall consider the D-theoretical framework to show that the antiferromagnetic system which arises in the strong coupling limit and at half filling corresponds to the principal chiral model in the continuum limit with dimensional reduction. Also pointed out that at strong coupling and half filling the system reduces to a Heisenberg antiferromagnet. This result is analogous to the result obtained in standard Hubbard model.},
     year = {2023}
    }
    

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  • TY  - JOUR
    T1  - Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation
    AU  - Subhamoy Singha Roy
    Y1  - 2023/02/24
    PY  - 2023
    N1  - https://doi.org/10.11648/j.ijhep.20231001.11
    DO  - 10.11648/j.ijhep.20231001.11
    T2  - International Journal of High Energy Physics
    JF  - International Journal of High Energy Physics
    JO  - International Journal of High Energy Physics
    SP  - 1
    EP  - 6
    PB  - Science Publishing Group
    SN  - 2376-7448
    UR  - https://doi.org/10.11648/j.ijhep.20231001.11
    AB  - It is pointed out that the low energy effective theory of a generalized spin system relates to the more generalized system shown by the Hubbard-like model. When the onsite repulsion is assumed to be provided by hard-core repulsion, a generalized fermion with flavour and colour degrees of freedom is used to define the Hubbard-like Hamiltonian in this case. In the strong coupling limit and at half filling this reduces to an antiferromagnet. The D-theory then helps us to associate the continuum limit of the (4+1)D aniferromagnet to 4D principal chiral model. It has been observed that in the strong coupling limit the problem of finding the ground state of lattice QCD is identical to that of solving the generalized antiferromagnet with Neel order playing the role of chiral symmetry breaking. In view of this, now formulate the Hubbard-like model Hamiltonian in terms of the gener- alized fermions with flavor and color degrees of freedom also shall consider the D-theoretical framework to show that the antiferromagnetic system which arises in the strong coupling limit and at half filling corresponds to the principal chiral model in the continuum limit with dimensional reduction. Also pointed out that at strong coupling and half filling the system reduces to a Heisenberg antiferromagnet. This result is analogous to the result obtained in standard Hubbard model.
    VL  - 10
    IS  - 1
    ER  - 

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Author Information
  • Department of Physics, JIS College of Engineering, Kalyani, India

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