holehop

◼ holehop[c, d] returns the hopping term in the case where one of the two operators is the hole (and not particle) creation operator.
◼ holehop[c, d, σ] returns the hopping term for spin σ electrons in the case where one of the two operators is the hole (and not particle) creation operator.

◼ Operators c and d must be expressed in a form which excludes the first index (creation/annihilation) and the last index (spin).

◼ See also: spinfliphop, hop, twohop.

Further examples

Load sneg and declared c and d to be fermionic operators

<< sneg`sneg`;
snegfermionoperators[c, d];

Hopping from an orbital to the occupied state of a band described by the operators (Subscript[c, k]). Note that annihilation of spin-up particle corresponds to lowering of spin by 1/2.

H = holehop[c[k], d[]]
holehop[c[k], d[], UP]
holehop[c[k], d[], DO]

The hole hopping operator does not commute with x and y components of the conventionally defined total spin operator.

{(Subscript[S, x]), (Subscript[S, y]), (Subscript[S, z]), SS} = 
        manyspin[{c[k], d[]}];
komutator[H, (Subscript[S, x])] // ExpandAll
komutator[H, (Subscript[S, y])] // ExpandAll
komutator[H, (Subscript[S, z])] // ExpandAll
komutator[H, SS] // ExpandAll