Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem

Evangelos Georgiou Filothodoros

doi:doi:10.11648/j.ijhep.20231002.11

Research Article |

| Peer-Reviewed

Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem

Evangelos Georgiou Filothodoros

Published in International Journal of High Energy Physics (Volume 10, Issue 2)

Received: 16 July 2023 Accepted: 3 August 2023 Published: 1 November 2023

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

I point out that the U(N) Chern-Simons 3d theory coupled to fermions at finite temperature and at a specific mean field approximation and the 3d Gross-Neveu model at finite temperature and imaginary chemical potential can give us the same results for the thermodynamic values of the free-energy and the saddle point equation for the thermal mass. I use specific results from the thermodynamics of fermionic models that coupled to Chern-Simons gauge field and imaginary chemical potential. In the latter case I introduce a representation for the canonical partition function for imaginary chemical potential and I see that the CS level κ plays the role of the U(1) charge. I further argue that the periodic structure of the imaginary chemical potential brings also Bloch’s theorem into the game. Namely, the vacuum structure of the fermionic system with imaginary baryon density is a Bloch wave. I further emphasise that Bloch waves correspond to fermionic (antisymmetric) or bosonic (symmetric) quasi- particles depending on the point in the band one sits in. This situation is similar with particles in a periodic potential of a crystal that behave like Bloch-wavefunctions. The overlap between them is a lattice momentum that can be restricted to the first Brillouin zone of the band structure.

Published in	International Journal of High Energy Physics (Volume 10, Issue 2)
DOI	10.11648/j.ijhep.20231002.11
Page(s)	12-19
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

Fermions, Chern-Simons, Bloch-wave

References

[1]	A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X6 (2016), no. 3 031043, [http://arxiv.org/abs/1606.01893].
[2]	J. Murugan and H. Nastase, Particle-vortex duality in topological insulators and superconductors, JHEP 05 (2017) 159, [http://arxiv.org/abs/1606.01912].
[3]	N. Seiberg, T. Senthil, C. Wang, and E. Witten, A Duality Web in 2+1 Dimensions and Condensed Matter Physics, Annals Phys. 374 (2016) 395–433, [http://arxiv.org/abs/1606.01989].
[4]	S. Kachru, M. Mulligan, G. Torroba, and H. Wang, Bosonization and Mirror Symmetry, Phys. Rev. D94 (2016), no. 8 085009, [http://arxiv.org/abs/1608.05077].
[5]	O. T˜A1 4rker, J. Van den Brink, T. Meng, FS. Nogueira, Bosonization in 2 + 1 dimensions viaChern-Simons bosonic particle-vortex duality, Phys. Rev. D102 (2020), 034506, [https://arxiv.org/abs/2004.10789].
[6]	S. Giombi, S. Minwalla, S. Prakash, S. P. Trivedi, S. R. Wadia, and X. Yin, Chern-Simons Theory with Vector Fermion Matter, Eur. Phys. J. C72 (2012) 2112, [http://arxiv.org/abs/1110.4386].
[7]	O. Aharony, S. Giombi, G. Gur-Ari, J. Maldacena, and R. Yacoby, The Thermal Free Energy in Large N Chern-Simons-Matter Theories, JHEP 03 (2013) 121, [http://arxiv.org/abs/1211.4843].
[8]	L. Alvarez-Gaume and D. Orlando and S. Reffert, Large charge at large N, Journal of High Energy Physics 12 (2019), [https://doi.org/10.1007/JHEP12(2019)142].
[9]	G. V. Dunne, Aspects of Chern-Simons theory, [https://doi.org/10.48550/arXiv.hep-th/9902115].
[10]	H. R. Christiansen, A. C. Petkou, M. B. Silva Neto, and N. D. Vlachos, On the thermodynamics of the (2+1)-dimensional Gross-Neveu model with complex chemical potential, Phys. Rev. D62 (2000) 025018, [http://arxiv.org/abs/hep-th/9911177].
[11]	S. Huang and B. Schreiber, Monopole Condensation, And Confinement In N=2 Supersymmetric Yang- Mills Theory, Nucl. Phys. B426, 644 (1994), [https://doi.org/10.48550/arXiv.hep-th/9407087].
[12]	J. Zinn-Justin, Quantum field theory and critical phenomena, Int. Ser. Monogr. Phys. 113 (2002).
[13]	E. G. Filothodoros, A. C. Petkou, and N. D. Vlachos, 3d fermion-boson map with imaginary chemical potential, Phys. Rev. D95 (2017), no. 6 065029, [http://arxiv.org/abs/1608.07795].
[14]	E. G. Filothodoros, Anastasios C. Petkou, Nicholas D. Vlachos, The fermion-boson map for large d, Nuclear Physics B 941 (2019) Pages 195-224, [http://arxiv.org/abs/1803.05950].
[15]	E. G. Filothodoros, The fermion-boson map at imaginary chemical potential in odd dimensions, [http://ikee.lib.auth.gr/record/303052/files/GRI-2019- 23684.pdf].
[16]	C. D. Fosco, G. L. Rossini, and F. A. Schaposnik, Induced parity breaking term in arbitrary odd dimensions at finite temperature, Phys. Rev. D59 (1999) 085012, [http://arxiv.org/abs/hep-th/9810199].
[17]	M. Barkeshli and J. McGreevy, Continuous transition between fractional quantum Hall and superfluid states, Phys. Rev. B89 (2014), no. 23 235116.
[18]	T. Li, L. Duca, M. Reitter, F. Grusdt, E. Demler, M. Endres, M. Schleier-Smith, I. Bloch, and U. Schneider, Bloch state tomography using wilson lines, Science 352 (2016) 1094.
[19]	E. G. Filothodoros, The fermion-boson map for large d and its connection to lattice transformations, [https://doi.org/10.48550/arXiv.2302.07013].

Cite This Article

Plain Text BibTeX RIS

APA Style

Evangelos Georgiou Filothodoros. (2023). Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem. International Journal of High Energy Physics, 10(2), 12-19. https://doi.org/10.11648/j.ijhep.20231002.11

Copy | Download

ACS Style

Evangelos Georgiou Filothodoros. Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem. Int. J. High Energy Phys. 2023, 10(2), 12-19. doi: 10.11648/j.ijhep.20231002.11

Copy | Download

AMA Style

Evangelos Georgiou Filothodoros. Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem. Int J High Energy Phys. 2023;10(2):12-19. doi: 10.11648/j.ijhep.20231002.11

Copy | Download

@article{10.11648/j.ijhep.20231002.11,
  author = {Evangelos Georgiou Filothodoros},
  title = {Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem},
  journal = {International Journal of High Energy Physics},
  volume = {10},
  number = {2},
  pages = {12-19},
  doi = {10.11648/j.ijhep.20231002.11},
  url = {https://doi.org/10.11648/j.ijhep.20231002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20231002.11},
  abstract = {I point out that the U(N) Chern-Simons 3d theory coupled to fermions at finite temperature and at a specific mean field approximation and the 3d Gross-Neveu model at finite temperature and imaginary chemical potential can give us the same results for the thermodynamic values of the free-energy and the saddle point equation for the thermal mass. I use specific results from the thermodynamics of fermionic models that coupled to Chern-Simons gauge field and imaginary chemical potential. In the latter case I introduce a representation for the canonical partition function for imaginary chemical potential and I see that the CS level κ plays the role of the U(1) charge. I further argue that the periodic structure of the imaginary chemical potential brings also Bloch’s theorem into the game. Namely, the vacuum structure of the fermionic system with imaginary baryon density is a Bloch wave. I further emphasise that Bloch waves correspond to fermionic (antisymmetric) or bosonic (symmetric) quasi- particles depending on the point in the band one sits in. This situation is similar with particles in a periodic potential of a crystal that behave like Bloch-wavefunctions. The overlap between them is a lattice momentum that can be restricted to the first Brillouin zone of the band structure.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem
AU  - Evangelos Georgiou Filothodoros
Y1  - 2023/11/01
PY  - 2023
N1  - https://doi.org/10.11648/j.ijhep.20231002.11
DO  - 10.11648/j.ijhep.20231002.11
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 12
EP  - 19
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20231002.11
AB  - I point out that the U(N) Chern-Simons 3d theory coupled to fermions at finite temperature and at a specific mean field approximation and the 3d Gross-Neveu model at finite temperature and imaginary chemical potential can give us the same results for the thermodynamic values of the free-energy and the saddle point equation for the thermal mass. I use specific results from the thermodynamics of fermionic models that coupled to Chern-Simons gauge field and imaginary chemical potential. In the latter case I introduce a representation for the canonical partition function for imaginary chemical potential and I see that the CS level κ plays the role of the U(1) charge. I further argue that the periodic structure of the imaginary chemical potential brings also Bloch’s theorem into the game. Namely, the vacuum structure of the fermionic system with imaginary baryon density is a Bloch wave. I further emphasise that Bloch waves correspond to fermionic (antisymmetric) or bosonic (symmetric) quasi- particles depending on the point in the band one sits in. This situation is similar with particles in a periodic potential of a crystal that behave like Bloch-wavefunctions. The overlap between them is a lattice momentum that can be restricted to the first Brillouin zone of the band structure.
VL  - 10
IS  - 2
ER  -

Copy | Download

Author Information

Evangelos Georgiou Filothodoros

Department of Nuclear and Elementary Particle Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Evangelos Georgiou Filothodoros. (2023). Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem. International Journal of High Energy Physics, 10(2), 12-19. https://doi.org/10.11648/j.ijhep.20231002.11

Copy | Download

ACS Style

Evangelos Georgiou Filothodoros. Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem. Int. J. High Energy Phys. 2023, 10(2), 12-19. doi: 10.11648/j.ijhep.20231002.11

Copy | Download

AMA Style

Evangelos Georgiou Filothodoros. Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem. Int J High Energy Phys. 2023;10(2):12-19. doi: 10.11648/j.ijhep.20231002.11

Copy | Download

@article{10.11648/j.ijhep.20231002.11,
  author = {Evangelos Georgiou Filothodoros},
  title = {Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem},
  journal = {International Journal of High Energy Physics},
  volume = {10},
  number = {2},
  pages = {12-19},
  doi = {10.11648/j.ijhep.20231002.11},
  url = {https://doi.org/10.11648/j.ijhep.20231002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20231002.11},
  abstract = {I point out that the U(N) Chern-Simons 3d theory coupled to fermions at finite temperature and at a specific mean field approximation and the 3d Gross-Neveu model at finite temperature and imaginary chemical potential can give us the same results for the thermodynamic values of the free-energy and the saddle point equation for the thermal mass. I use specific results from the thermodynamics of fermionic models that coupled to Chern-Simons gauge field and imaginary chemical potential. In the latter case I introduce a representation for the canonical partition function for imaginary chemical potential and I see that the CS level κ plays the role of the U(1) charge. I further argue that the periodic structure of the imaginary chemical potential brings also Bloch’s theorem into the game. Namely, the vacuum structure of the fermionic system with imaginary baryon density is a Bloch wave. I further emphasise that Bloch waves correspond to fermionic (antisymmetric) or bosonic (symmetric) quasi- particles depending on the point in the band one sits in. This situation is similar with particles in a periodic potential of a crystal that behave like Bloch-wavefunctions. The overlap between them is a lattice momentum that can be restricted to the first Brillouin zone of the band structure.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Fermions Coupled to Chern-Simons Gauge Field or Imaginary Chemical Potential and the Bloch Theorem
AU  - Evangelos Georgiou Filothodoros
Y1  - 2023/11/01
PY  - 2023
N1  - https://doi.org/10.11648/j.ijhep.20231002.11
DO  - 10.11648/j.ijhep.20231002.11
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 12
EP  - 19
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20231002.11
AB  - I point out that the U(N) Chern-Simons 3d theory coupled to fermions at finite temperature and at a specific mean field approximation and the 3d Gross-Neveu model at finite temperature and imaginary chemical potential can give us the same results for the thermodynamic values of the free-energy and the saddle point equation for the thermal mass. I use specific results from the thermodynamics of fermionic models that coupled to Chern-Simons gauge field and imaginary chemical potential. In the latter case I introduce a representation for the canonical partition function for imaginary chemical potential and I see that the CS level κ plays the role of the U(1) charge. I further argue that the periodic structure of the imaginary chemical potential brings also Bloch’s theorem into the game. Namely, the vacuum structure of the fermionic system with imaginary baryon density is a Bloch wave. I further emphasise that Bloch waves correspond to fermionic (antisymmetric) or bosonic (symmetric) quasi- particles depending on the point in the band one sits in. This situation is similar with particles in a periodic potential of a crystal that behave like Bloch-wavefunctions. The overlap between them is a lattice momentum that can be restricted to the first Brillouin zone of the band structure.
VL  - 10
IS  - 2
ER  -

Copy | Download