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

TLDR: In this article, a multi-targeted density matrix renormalization group method was proposed for computing ground states of local, gapped Hamiltonians, particularly in one dimension, where the use of a block or banded Lanczos algorithm allows for the simultaneous, variational optimization of the bundle of excitations.

Abstract: 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 density matrix renormalization group 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.