Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit

Subhamoy Singha Roy

doi:doi:10.11648/j.ijhep.20231001.12

| Peer-Reviewed

Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.

Published in	International Journal of High Energy Physics (Volume 10, Issue 1)
DOI	10.11648/j.ijhep.20231001.12
Page(s)	7-11
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

Skyrmionic Excitation, QCD, Antiferromagnetic Order, D-theory, Non-Abelian Gauge Field

References

[1]	J. Hubbard: Proc. Roy. Soc. A 276, 238 (1963).
[2]	B. Basu, S. Dhar and P. Bandyopadhyay: Phys. Rev. B 69, 094505 (2004).
[3]	J. Gonzalez, M. A. Martin-Delgado, G. Sierra, A. H. Vozmediano: Quantum Electron Liquids and High-T_c Superconductivity (Springer, Berlin).
[4]	A. P. Balachandran, E. Ercolessi, G. Morandi, A. M. Srivastava: Hubbard Model and Anyon Superconductivity (World Scientific).
[5]	N. Read and S. Sachdev: Nucl. Phys. B 316, 609 (1989).
[6]	S. Radjbar-Daemi, A. Salam and J. Strathdee: Phys. Rev. B 48, 3190 (1993).
[7]	For a review, see J. Kogut: Rev. Mod. Phys. 55, 775 (1980).
[8]	E. Langmann and G. Semenoff: Phys. Lett. B 297, 175 (1992).
[9]	M. C. Diamantini, P. Sodano, E. Langmann and G. Semenoff: Nucl. Phys. B 406, 595 (1993).
[10]	G. Goswami and P. Bandyopadhyay: J. Math. Phys. 38, 4451 (1997).
[11]	P. Bandyopadhyay: Int. J. Mod. Phys. A 15, 4107 (2000).
[12]	M. Imachi et. al.: Prog. Theo. Phys. Suppl. 48, 101 (1971).
[13]	P. Bandyopadhyay and S. S. De: Nuovo Cimento 27A, 294 (1975).
[14]	P. Bandyopadhyay and J. Mahalanobis: Phys. Rev. C 27, 628 (1983).
[15]	J. Mahalanobis and P. Bandyopadhyay: Phys. Rev. C 31, 1241 (1985).
[16]	E. Nelson: Phys. Rev. 50, 1079 (1966); Dynamical Theory of Brownian Motion (Princeton University Press 1967).
[17]	P. Bandyopadhyay and K. Hajra: J. Math. Phys. 28, 711 (1987).
[18]	K. Hajra and P. Bandyopadhyay: Phys. Lett. A 155, 7 (1991).
[19]	P. Bandyopadhyay: Int. J. Theor. Phys. 39, 2677 (2000).
[20]	G.’tHooft: Nucl. Phys. B 72, 461 (1974).
[21]	E. Witten: Nucl. Phys. B 160, 57 (1979).
[22]	S. Singha Roy and P. Bandyopadhyay,: Phys. Lett. A 382,1973 (2018).
[23]	S. S. Roy and P. Bandyopadhyay, Phys. Lett. A 337,2884 (2013).
[24]	T. J. Osborne, M. A. Nielson, Phys. Rev. A, 66, 032110 (2002).

Cite This Article

Plain Text BibTeX RIS

APA Style

Subhamoy Singha Roy. (2023). Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit. International Journal of High Energy Physics, 10(1), 7-11. https://doi.org/10.11648/j.ijhep.20231001.12

Copy | Download

ACS Style

Subhamoy Singha Roy. Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit. Int. J. High Energy Phys. 2023, 10(1), 7-11. doi: 10.11648/j.ijhep.20231001.12

Copy | Download

AMA Style

Subhamoy Singha Roy. Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit. Int J High Energy Phys. 2023;10(1):7-11. doi: 10.11648/j.ijhep.20231001.12

Copy | Download

@article{10.11648/j.ijhep.20231001.12,
  author = {Subhamoy Singha Roy},
  title = {Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit},
  journal = {International Journal of High Energy Physics},
  volume = {10},
  number = {1},
  pages = {7-11},
  doi = {10.11648/j.ijhep.20231001.12},
  url = {https://doi.org/10.11648/j.ijhep.20231001.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20231001.12},
  abstract = {It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit
AU  - Subhamoy Singha Roy
Y1  - 2023/02/24
PY  - 2023
N1  - https://doi.org/10.11648/j.ijhep.20231001.12
DO  - 10.11648/j.ijhep.20231001.12
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 7
EP  - 11
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20231001.12
AB  - It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.
VL  - 10
IS  - 1
ER  -

Copy | Download

Author Information

Subhamoy Singha Roy

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Subhamoy Singha Roy. (2023). Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit. International Journal of High Energy Physics, 10(1), 7-11. https://doi.org/10.11648/j.ijhep.20231001.12

Copy | Download

ACS Style

Subhamoy Singha Roy. Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit. Int. J. High Energy Phys. 2023, 10(1), 7-11. doi: 10.11648/j.ijhep.20231001.12

Copy | Download

AMA Style

Subhamoy Singha Roy. Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit. Int J High Energy Phys. 2023;10(1):7-11. doi: 10.11648/j.ijhep.20231001.12

Copy | Download

@article{10.11648/j.ijhep.20231001.12,
  author = {Subhamoy Singha Roy},
  title = {Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit},
  journal = {International Journal of High Energy Physics},
  volume = {10},
  number = {1},
  pages = {7-11},
  doi = {10.11648/j.ijhep.20231001.12},
  url = {https://doi.org/10.11648/j.ijhep.20231001.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20231001.12},
  abstract = {It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit
AU  - Subhamoy Singha Roy
Y1  - 2023/02/24
PY  - 2023
N1  - https://doi.org/10.11648/j.ijhep.20231001.12
DO  - 10.11648/j.ijhep.20231001.12
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 7
EP  - 11
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20231001.12
AB  - It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.
VL  - 10
IS  - 1
ER  -

Copy | Download