Many-body scars in multiband Majorana fermion systems

In some quantum systems, the Hilbert space breaks up into a large ergodic sector and a smaller scar subspace. They may sometimes be distinguished by their transformation under a group whose rank grows with the system size. The quantum many-body scars are invariant under this group, while all other states are not. We apply this idea to lattice systems with N sites and M Majorana fermions per site. We identify two families of scars that are SO(N)-invariant. For M=4, where our construction reduces to spin-1/2 fermions, they are the eta-pairing states and the states of maximum spin. For M=6 we derive exact scar wavefunctions and entanglement entropy. It grows logarithmically with the sub-system size. We argue that any group-invariant scars generally have the entanglement entropy parametrically smaller than that of generic states. The scars energies are not equidistant in general but can be made so. With local Hamiltonians the scars typically have certain degeneracies. The scar spectrum can be made ergodic by adding a non-local interaction term. Because the number of scars grows exponentially with M, they make a sizable contribution to the density of states for small N.