How to implement symmetry which anticommutes with hamiltonian

Question

Dear community,

How is it possible to implement the conservation of an anti-block structure for {H,U} = 0?

Let us consider for instance the example H = ∑ σˣᵢ + ∑ σˣᵢ σˣⱼ σˣₖ with U = ∏ σˣᵢ where the z-parity only anticommutes with the hamiltonian. Right now I am implementing this using the square of the Hamiltonian, since then [H²,U]=0 and we can use regular quantum numbers; however, this is a very bad solution. Can you think of a better way?

Best,

v.

Comments

Hi, I'm not sure I'll be able to give a helpful answer to this, but is there any reference you could provide for the concept of an anti-block structure?