On Lieb-Robinson Bounds for the Double Bracket Flow

Understand

We consider the possibility of developing a Lieb-Robinson bound for the double bracket flow.

• This is a differential equation $$\partial_B H(B)=[[V,H(B)],H(B)]$$ which may be used to diagonalize Hamiltonians.
• Here, $V$ is fixed and $H(0)=H$.
• We argue (but do not prove) that $H(B)$ need not converge to a limit for nonzero real $B$ in the infinite volume limit, even assuming several conditions on $H(0)$.