Implicitly disentangled renormalization

TL;DR

This paper introduces a local operator-based real-space RG method for quantum lattice states that removes short-range entanglement without disentanglers, improving tensor network algorithms and achieving scale invariance at criticality.

Contribution

It presents a novel RG approach that avoids disentanglers by using only local operators, enhancing efficiency in quantum many-body system analysis.

Findings

Successfully applied to 1D critical ground states

Achieves scale-invariant fixed points

Potentially improves tensor network algorithms

Abstract

We propose a new implementation of real-space renormalization group (RG) transformations for quantum states on a lattice. Key to this approach is the removal of short-ranged entanglement, similar to Vidal's entanglement renormalization (ER), which allows a proper RG flow to be achieved. However, our proposal only uses operators that act locally within each block, such that the use of disentanglers acting across block boundaries is not required. By avoiding the use of disentanglers we argue many tensor network algorithms for studying quantum many-body systems can be significantly improved. The effectiveness of this RG approach is demonstrated through application to the ground state of a 1D system at criticality, which is shown to reach a scale-invariant fixed point.