LadderOperators.jl

Generate matrix representation of fermionic and bosonic ladder operators on the full Fock-space with $N$ lattice sites. Provide additional routines to reduce to U(1)-blocks with fixed particle number for Fermions. Code developed to study Hubbard-Dimer in multimode cavity, hence the focus is not on the performance of the implementation, but rather on ease of use.

The matrix representation is generated using the Jordan-Wigner strings in an MPS like approach. Ladder operators act as

so that their matrix representation in a site resolved Slater-Basis reads

By implementing the site-local representation of $c_i^\dagger$, one can evaluate the representation on the full Fock space by calculating the associated Kronecker products. For spinless-fermions, with site local basis $|0\rangle, |1\rangle$ the site local representation reads

The representation of additional internal structure, like spins, is performed by treating these degrees of freedom like lattice sites as well.

Implemented are spinless fermions, spinful fermions, multi_band spinful fermions as well as bosons. The corresponding ladder operators can be obtained using the ladder_operators function.