Fermions, strings, and gauge fields in lattice spin models

@article{Levin2003FermionsSA,
  title={Fermions, strings, and gauge fields in lattice spin models},
  author={Michael Levin and Xiao-Gang Wen},
  journal={Physical Review B},
  year={2003},
  volume={67},
  pages={245316}
}
We investigate the general properties of lattice spin models with emerging fermionic excitations. We argue that fermions always come in pairs and their creation operator always has a stringlike structure with the newly created particles appearing at the end points of the string. The physical implication of this structure is that the fermions always couple to a nontrivial gauge field. We present exactly soluble examples of this phenomenon in two and three dimensions. Our analysis is based on an… 
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References

SHOWING 1-10 OF 23 REFERENCES
Phys
  • Rev. Lett. 90, 016803
  • 2003
Phys
  • Rev. B 65, 224412
  • 2002
Phys
  • Rev. Lett. 89, 277004
  • 2002
Phys
  • Rev. Lett. 86, 1881
  • 2001
Nucl
  • Phys. Proc. Suppl. 68, 1
  • 1998
Advances in Physics 44
  • 405
  • 1995
Phys
  • Rev. Lett. 66, 1773
  • 1991
Phys
  • Rev. B 44, 2664
  • 1991
Phys
  • Rev. B 39, 11413
  • 1989
Phys
  • Rev. B 40, 7133
  • 1989
...
1
2
3
...