BooksStandalone TitlesCollected Volumepp. 515–525

On Lieb–Robinson bounds for the double bracket flow

  • Matthew B. Hastings

    Microsoft Quantum Santa Barbara; and Microsoft Research, Redmond, United States of America
On Lieb–Robinson bounds for the double bracket flow cover
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Abstract

We consider the possibility of developing a Lieb–Robinson bound for the double bracket flow (Brockett, 1991; Chu and Driessel, 1990). This is a differential equation BH(B)=[[V,H(B)],H(B)]{\partial_{B}H(B)\mkern 1.0mu{=}\mkern2mu[[V,H(B)]},{H(B)]} which may be used to diagonalize Hamiltonians. Here, VV is fixed and H(0)=HH(0)=H. We argue (but do not prove) that H(B)H(B) need not converge to a limit for nonzero real BB in the infinite volume limit, even assuming several conditions on H(0)H(0). However, we prove Lieb–Robinson bounds for all BB for the double bracket flow for free fermion systems, but the range increases exponentially with the control parameter BB.