spinfliphop

◼ spinfliphop[c, d] returns the electron hopping with spin flip operator between the levels described by the operators c and d.

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

◼ See also: holehop, hop, twohop.

Further examples

Load sneg and declared c and d to be fermionic operators

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

Check definition

H = spinfliphop[c[], d[]]

The spin flip hopping operator breaks SU(2) symmetry in the spin space. It does, however, commute with the (Subscript[S, x]) operator, so a U(1) subgroup of SU(2) is still a symmetry group of models with spin-flip hopping.

{(Subscript[S, x]), (Subscript[S, y]), (Subscript[S, z]), SS} = 
        manyspin[{c[], d[]}];
komutator[H, (Subscript[S, x])] == 0 // ExpandAll
komutator[H, (Subscript[S, y])] // ExpandAll
komutator[H, (Subscript[S, z])] // ExpandAll
komutator[H, SS] // ExpandAll

Some (super)-commutators of spin-flip hopping term

superkomutator[(Subscript[S, y]), H, 1] // Expand
superkomutator[(Subscript[S, y]), H, 2] // Expand

By rotating the spin-flip hopping term around the y-axis in the spin space, we obtain a spin preserving hopping term with different signs for spin-up and spin-down electrons. Note the use of the block wrapper to prevent the automatic distribution over the terms in H.

α = Pi/2
U = Exp[I α (Subscript[S, y])]
nc[conj[U], block[H], U]