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

TL;DR

This paper introduces a multi-targeted DMRG method using block Lanczos to efficiently compute multiple excitations in matrix product states, enabling accurate local observables with small bond dimensions.

Contribution

It presents a novel approach combining block Lanczos with MPS to optimize many excitations simultaneously, improving efficiency and accuracy.

Findings

Effective in computing many excitations at low bond dimension

Reliable local observables across the chain

Demonstrated on Heisenberg and other models

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.