A real space decoupling transformation for quantum many-body systems

TL;DR

This paper introduces a real space renormalization group method that explicitly decouples many-body quantum systems into independent parts, facilitating efficient simulation of highly entangled phases and advancing understanding of quantum matter.

Contribution

It presents a novel real space decoupling transformation based on entanglement renormalization, enabling explicit separation of degrees of freedom in quantum many-body systems.

Findings

Successfully decouples ground state of a critical quantum spin chain

Demonstrates analytical and numerical feasibility of the approach

Provides generalized concepts of RG flow and scale invariance

Abstract

We propose a real space renormalization group method to explicitly decouple into independent components a many-body system that, as in the phenomenon of spin-charge separation, exhibits separation of degrees of freedom at low energies. Our approach produces a branching holographic description of such systems that opens the path to the efficient simulation of the most entangled phases of quantum matter, such as those whose ground state violates a boundary law for entanglement entropy. As in the coarse-graining transformation of [Phys. Rev. Lett. 99, 220405 (2007)], the key ingredient of this decoupling transformation is the concept of entanglement renormalization, or removal of short-range entanglement. We demonstrate the feasibility of the approach, both analytically and numerically, by decoupling in real space the ground state of a critical quantum spin chain into two. Generalized notions of RG flow and of scale invariance are also put forward.