Direct solution of multiple excitations in a matrix product state with block Lanczos*

Matrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one dimension.  We introduce the multi-targeted method that acts on a bundled matrix product state, holding many excitations.  The use of a block or banded Lanczos algorithm allows for the simultaneous, variational optimization of the bundle of excitations.  The method is demonstrated on a Heisenberg model and other cases of interest.  A large of number of excitations can be obtained at a small bond dimension with highly reliable local observables throughout the chain.