Controlled bond expansion for DMRG ground state search at single-site costs

TL;DR

This paper introduces a controlled bond expansion algorithm for DMRG that achieves two-site accuracy at single-site computational costs, enabling efficient symmetry sector adjustments during ground state searches.

Contribution

The authors develop a novel controlled bond expansion method for DMRG that maintains variational accuracy with minimal computational overhead, improving upon traditional single-site and two-site approaches.

Findings

CBE-DMRG accurately captures phase differences in the Kondo-Heisenberg model.

The algorithm identifies significant orthogonal space components for bond expansion.

CBE-DMRG operates without mixing parameters, ensuring variational consistency.

Abstract

DMRG ground state search algorithms employing symmetries must be able to expand virtual bond spaces by adding or changing symmetry sectors if these lower the energy. Traditional single-site DMRG does not allow bond expansion; two-site DMRG does, but at much higher computational costs. We present a controlled bond expansion (CBE) algorithm that yields two-site accuracy and convergence per sweep, at single-site costs. Given a matrix product state $\Psi$ defining a variational space, CBE identifies parts of the orthogonal space carrying significant weight in $H\Psi$ and expands bonds to include only these. CBE-DMRG uses no mixing parameters and is fully variational. Using CBE-DMRG, we show that the Kondo-Heisenberg model on a width 4 cylinder features two distinct phases differing in their Fermi surface volumes.