Augmenting Density Matrix Renormalization Group with Disentanglers

TL;DR

This paper introduces a novel DMRG-based ansatz augmented with disentanglers, enabling efficient simulation of two-dimensional quantum systems with area-law entanglement scaling, thus extending DMRG's applicability beyond narrow systems.

Contribution

The authors propose a new ansatz combining DMRG with disentanglers to encode area-law entanglement, maintaining low computational cost while improving 2D system simulation.

Findings

Successfully benchmarked on 2D transverse Ising model

Achieved area-law entanglement scaling in the new ansatz

Extended DMRG applicability to wider 2D systems

Abstract

Density Matrix Renormalization Group (DMRG) and its extensions in the form of Matrix Product States (MPS) are arguably the choice for the study of one dimensional quantum systems in the last three decades. However, due to the limited entanglement encoded in the wave-function ansatz, to maintain the accuracy of DMRG with the increase of the system size in the study of two dimensional systems, exponentially increased resources are required, which limits the applicability of DMRG to only narrow systems. In this work, we introduce a new ansatz in which DMRG is augmented with disentanglers to encode area-law-like entanglement entropy (entanglement entropy supported in the new ansatz scales as $l$ for a $l \times l$ system). In the new method, the $O(D^3)$ low computational cost of DMRG is kept (with an overhead of $O(d^4)$ and $d$ the dimension of the physical degree of freedom). We perform benchmark calculations with this approach on the two dimensional transverse Ising and Heisenberg models. This new ansatz extends the power of DMRG in the study of two-dimensional quantum systems.