Reply to comment on "Controlled bond expansion for Density Matrix Renormalization Group ground state search at single-site costs"

TL;DR

This paper defends the controlled bond expansion method for DMRG ground state search against critiques, emphasizing the importance of projections and demonstrating the combined approach's efficiency and robustness.

Contribution

The authors clarify the significance of projections in CBE-DMRG and advocate for combining CBE with 3S mixing for improved performance.

Findings

Omitting the projection introduces avoidable errors in TDVP.

Combining CBE with 3S mixing enhances efficiency and robustness.

Examples demonstrate the superiority of the combined method.

Abstract

We reply to McCulloch and Osborne's recent comment on our manuscript (Phys. Rev. Lett. 130, 246402 (2023)) on controlled bond expansion (CBE) for density matrix renormalization group (DMRG) ground state search. We appreciate their suggestion to consider randomized SVD and address their constructive critique on the variational properties of CBE-DMRG. However, we strongly disagree with their proposal to omit the projection to the 2-site tangent space and explain its importance for efficient bond expansion. In particular, in the context of CBE applied to the time-dependent variational principle (TDVP), we show that omitting this projection can lead to avoidable errors. Lastly, we emphasize the complementary roles of 3S mixing and CBE, reiterating our recommendation from Phys. Rev. Lett. 130, 246402 (2023) to combine both methods (CBE+$\alpha$). We provide examples to demonstrate the superior efficiency and robustness of CBE+$\alpha$.