# On Lieb-Robinson Bounds for the Double Bracket Flow

@inproceedings{Hastings2022OnLB, title={On Lieb-Robinson Bounds for the Double Bracket Flow}, author={Matthew B. Hastings}, year={2022} }

We consider the possibility of developing a Lieb-Robinson bound for the double bracket flow[3, 4]. This is a differential equation m ( ) = [[+, ( )], ( )] which may be used to diagonalize Hamiltonians. Here, + is fixed and (0) = . We argue (but do not prove) that ( ) need not converge to a limit for nonzero real in the infinite volume limit, even assuming several conditions on (0). However, we prove Lieb-Robinson bounds for all for the double-bracket flow for free fermion systems, but the range…

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