Fermions, strings, and gauge fields in lattice spin models

@article{Levin2003FermionsSA,
  title={Fermions, strings, and gauge fields in lattice spin models},
  author={Michael A. 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… Expand
View PDF on arXiv
112 Citations
Highly Influential Citations
3
Background Citations
21
Methods Citations
5
Results Citations
1

Figures from this paper

112 Citations

Citation Type

Citation Type

Family of non-Abelian Kitaev models on a lattice: Topological condensation and confinement
We study a family of non-Abelian topological models in a lattice that arise by modifying the Kitaev model through the introduction of single-qudit terms. The effect of these terms amounts to a… Expand
Realizing non-Abelian statistics in time-reversal-invariant systems
We construct a series of $(2+1)$-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport of quasiparticles is described by using a correspondence between the… Expand
Nonperturbative definition of the standard models
The Standard Models contain chiral fermions coupled to gauge theories. It has been a long-standing problem to give such gauged chiral fermion theories a quantum non-perturbative definition. By… Expand
Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions
We construct fixed point lattice models for group supercohomology symmetry protected topological (SPT) phases of fermions in 2+1D. A key feature of our approach is to construct finite depth circuits… Expand
Quantum ether: photons and electrons from a rotor model
We give an example of a purely bosonic model--a rotor model on the 3D cubic lattice--whose low energy excitations behave like massless U(1) gauge bosons and massless Dirac fermions. This model can be… Expand
Anyonic loops in three-dimensional spin liquid and chiral spin liquid
We established a large class of exactly soluble spin liquids and chiral spin liquids on three-dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact… Expand
String-net condensation: A physical mechanism for topological phases
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''… Expand
Topological color codes and two-body quantum lattice Hamiltonians
Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with… Expand
Perturbative approach to an exactly solved problem: Kitaev honeycomb model
We analyze the gapped phase of the Kitaev honeycomb model perturbatively in the isolated-dimer limit. Our analysis is based on the continuous unitary transformations method which allows one to… Expand
Topological edge states in a one-dimensional ladder system
In this thesis, an interacting, particle number conserving model of spinless fermions in a two-leg ladder system is analyzed in the context of topological edge states. As proven in [1], where the… Expand
...
1
2
3
4
5
...

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
...