Models noninteracting fermions

For Jz = 0, as stated above, H is equivalent to a noninteracting gas of spinless fermions, which for low energy phenomena is equivalent to a noninteracting Luttinger model. 

Throughout this book electronic models of conjugated polymers are developed within the number or second quantization representation. This representation is particularly powerful for treating many-body problems. However, as it is less familiar than a first quantization approach, this appendix explains the equivalence of the two approaches for single particle Hamiltonians. We take two examples the fermion noninteracting (or Hiickel) Hamiltonian and the exciton transfer model. 

In ID, the fermion sign problem can actually be eliminated completely. In lattice models of electronic systems, this is accomplished by a trick called the checkerboard decomposition. This method is best illustrated using noninteracting... 

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