Fermion basis

The fermionBasis class defines the fermionic basis and the quantum-number sectors used to build and block-diagonalize impurity Hamiltonians. It provides the symmetry structure used throughout the NRG solver setup.

How the basis is constructed

The constructor starts from dof fermionic orbitals and builds their many-body occupation basis. Each orbital’s creation matrix is assembled with Kronecker products; the sigz factors supply the signs needed for fermionic anticommutation between orbitals. Applying each creation operator and its adjoint gives the occupation values stored for every basis state.

The selected modelSymmetry then determines the quantum-number vector assigned to each state:

• chargeOnly groups states by total particle number.

• spinOnly groups by the difference between the configured up- and down-orbital occupations.

• chargeAndSpin keeps the up- and down-orbital occupation counts as separate quantum numbers.

States with identical quantum-number vectors are collected into blocks. The class uses those block indices to convert full-space operators into qOperator objects containing only nonzero sector-to-sector matrices. set_f_dag_operators applies this conversion to the fermion creation operators. The same machinery is available through get_block_operators for other operators. get_block_Hamiltonian extracts diagonal sector blocks and checks that the input Hamiltonian is Hermitian and has no couplings between distinct quantum-number sectors.

This class constructs basis and operator structure; the impurity or bath model builds its Hamiltonian and passes it through these block operations.

For the generated class reference, see the fermionBasis class documentation.