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

Subhamoy Singha Roy

doi:doi:10.11648/j.ijhep.20231001.11

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

Subhamoy Singha Roy

Published in International Journal of High Energy Physics (Volume 10, Issue 1)

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), 2024. Published by Science Publishing Group

Keywords

Hubbard Model, Antiferromagnet, D- Framework, Chiral Breaking

References

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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

Subhamoy Singha Roy

Department of Physics, JIS College of Engineering, Kalyani, India

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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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download