Entanglement renormalization

TL;DR

This paper introduces a new real-space renormalization method for quantum lattice systems that efficiently manages entanglement, enabling the analysis of large systems with minimal computational resources.

Contribution

It proposes a novel entanglement-based coarse-graining scheme that keeps the Hilbert space dimension bounded, allowing scalable analysis of quantum critical systems.

Findings

Efficiently addresses tens of thousands of spins with logarithmic scaling.

Reveals layered organization of entanglement across length scales.

Shows each length scale contributes equally to entanglement at criticality.

Abstract

In the context of real-space renormalization group methods, we propose a novel scheme for quantum systems defined on a D-dimensional lattice. It is based on a coarse-graining transformation that attempts to reduce the amount of entanglement of a block of lattice sites before truncating its Hilbert space. Numerical simulations involving the ground state of a 1D system at criticality show that the resulting coarse-grained site requires a Hilbert space dimension that does not grow with successive rescaling transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each rellevant length scale makes an equivalent contribution to the entanglement of a block with the rest of the system.