Skip to main content
Log in

Superfrustration of charge degrees of freedom

  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We review recent results, obtained with P. Fendley, on frustration of quantum charges in lattice models for itinerant fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to models possessing supersymmetry. In such models frustration takes the form of what we call superfrustration: an extensive degeneracy of supersymmetric ground states. We present a gallery of examples of superfrustration on a variety of 2D lattices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E.J.W. Verwey, Nature (London) 144, 327 (1939); P.W. Anderson, Phys. Rev. 102, 1008 (1956); G.H. Wannier, Phys. Rev. 79, 357 (1950)

    Article  ADS  Google Scholar 

  2. E. Runge, P. Fulde, Phys. Rev. B 70, 245113 (2004); O.I. Motrunich, P.A. Lee, Phys. Rev. B 69, 214516 (2004)

    Article  ADS  Google Scholar 

  3. P. Fendley, K. Schoutens, Phys. Rev. Lett. 95, 046403 (2005); e-print arXiv:hep-th/0504595

    Article  ADS  Google Scholar 

  4. P. Fendley, K. Schoutens, J. de Boer, Phys. Rev. Lett. 90, 120402 (2003); e-print arXiv:hep-th/0210161

    Article  ADS  MathSciNet  Google Scholar 

  5. P. Fendley, B. Nienhuis, K. Schoutens, J. Phys. A 36, 12399 (2003); e-print arXiv:cond-mat/0307338

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. E. Witten, Nucl. Phys. B 202, 253 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  7. M. Beccaria, G. F. De Angelis, Phys. Rev. Lett. 94, 100401 (2005); e-print arXiv:cond-mat/0407752

    Article  ADS  Google Scholar 

  8. R. Bott, L.W. Tu, Differential Forms in Algebraic Topology, GTM 82 (Springer Verlag, New York, 1982)

    MATH  Google Scholar 

  9. H.B. Thacker, Rev. Mod. Phys. 53, 253 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  10. D. Friedan, S.H. Shenker, C. Itzykson, H. Saleur, J.B. Zuber, in Conformal invariance and applications to statistical mechanics (World Scientific, 1988)

  11. G. Veneziano, J. Wosiek, JHEP 0611, 030 (2006); e-print arXiv:hep-th/0609210

    Article  ADS  MathSciNet  Google Scholar 

  12. H. van Eerten, J. Math. Phys. 46, 123302 (2005); e-print arXiv:cond-mat/0509581

    Article  ADS  MathSciNet  Google Scholar 

  13. J. Jonsson, Electronic Journal of Combinatorics 13, #R67 (2006); Certain Homology Cycles of the Independence Complex of Grid Graphs, Preprint (October 2005)

  14. L. Huijse, J. Halverson, P. Fendley, K. Schoutens, Charge frustration and quantum criticality for strongly correlated fermions, Preprint (April 2008); e-print arXiv:0804.0174

  15. P.W. Kasteleyn, J. Math. Phys. 4, 287 (1963); F.Y. Wu, Phys. Rev. 168, 539 (1967)

    Article  ADS  MathSciNet  Google Scholar 

  16. P. Fendley, K. Schoutens, H. van Eerten, J. Phys. A 38, 315 (2005); e-print arXiv:cond-mat/0408497

  17. M. Bousquet-Melou, S. Linusson, E. Nevo, On the independence complex of square grids, Preprint (2007); e-print arXiv:math/0701890

  18. J. Jonsson, Hard Squares on Grids With Diagonal Boundary Conditions, Preprint (August 2006)

  19. R.J. Baxter, Hard squares for z = −1, Preprint (2007); e-print arXiv:0709.4324v2

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. Huijse.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huijse, L., Schoutens, K. Superfrustration of charge degrees of freedom. Eur. Phys. J. B 64, 543–550 (2008). https://doi.org/10.1140/epjb/e2008-00150-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2008-00150-9

PACS

Navigation