TKNN formula for general Hamiltonian

@inproceedings{Fukaya2019TKNNFF,
  title={TKNN formula for general Hamiltonian},
  author={Hidenori Fukaya and Tetsuya Onogi and Satoshi Yamaguchi and Xi Wu},
  year={2019}
}
Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low energy effective action for a general class of Hamiltonians bilinear in the fermion with general U(1) gauge interactions including non-minimal couplings by an explicit calculation. A series of Ward-Takahashi identities are crucial to relate the Chern-Simons level… 

References

SHOWING 1-10 OF 18 REFERENCES

Induced Chern-Simons Class with Lattice Fermions

During the past several years there has been a growing interest in 3-dimensional gauge theories as high temperature field theories l )-5) and as dynamics for planar systems such as the quantum Hall

Quantized Hall conductance as a topological invariant.

TLDR
The new formulation generalizes the earlier result and draws the conclusion that there must be a symmetry breaking in the many-body ground state when applying to the fractional quantized Hall effect.

Induced Topological Invariants by Lattice Fermions in Odd Dimensions

On etudie la contribution fermionique aux champs de jauge externe dans un espace temps de dimension impaire avec fermion de Wilson reticule pour obtenir l'invariant topologique, de la classe de

Topological field theory of time-reversal invariant insulators

We show that the fundamental time-reversal invariant (TRI) insulator exists in $4+1$ dimensions, where the effective-field theory is described by the $(4+1)$-dimensional Chern-Simons theory and the

Three Lectures On Topological Phases Of Matter

These notes are based on lectures at the PSSCMP/PiTP summer school that was held at Princeton University and the Institute for Advanced Study in July, 2015. They are devoted largely to topological

Axial anomaly in three dimensions and planar fermions.

  • Ishikawa
  • Physics
    Physical review. D, Particles and fields
  • 1985
The origin and implications of the axial anomaly in three dimensions for fermions are discussed. Since the zero eigenvalue of the Dirac equation makes the partition function vanish, it is a singular