Quantum scars viewed as common eigenstates of simple bipartitions of scarred Hamiltonians and relations to quantum cellular automata.

We discuss two new perspectives on quantum scars.

First, we show that for a large class of scarred models, the scarred states turn out to be common eigenstates of simple bipartitions A,B of the Hamiltonian (H = A + B). Provided the additional constraint e^-iAn = e^-iBn = I is satisfied for some positive integer n, it can be shown that the common eigenstates (scarred states) must have equidistant energies, and thus exhibit perfect many-body revivals. We find that this picture applies to a large class of quantum scars derived from quasiparticle methods.

Second, we show how the above conditions can be related to simple quantum cellular automata. Indeed, the common eigenstates of the above bipartitions generate a subspace that evolves in time according to a simple quantum cellular automaton represented by T = e^-iA e^-iB . We exploit this connection to construct non-integrable Hamiltonians H = A + B that host quantum scars, where the scarred states are in one-to-one correspondence with trivial many-body revivals of the corresponding automaton. This method not only allows for the construction of new models hosting exact quantum scars, but, as we show, also provides a way to design approximate quantum scars and estimate their decay time scale without the need of an explicit small parameter. Notably, we find that this picture applies to the well-known PXP model.