Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms

TL;DR

This paper compares entanglement renormalization in real space with traditional momentum-space RG in harmonic lattice systems, analyzing their effectiveness in capturing critical behavior and fixed points in quantum systems.

Contribution

It provides a detailed comparison of real-space entanglement renormalization and momentum-space RG, highlighting their differences and similarities in quantum lattice models.

Findings

ER generates a proper real-space RG flow in harmonic systems

Comparison shows ER captures critical fixed points effectively

Analysis of relevant and irrelevant perturbations in RG flows

Abstract

The ability of entanglement renormalization (ER) to generate a proper real-space renormalization group (RG) flow in extended quantum systems is analysed in the setting of harmonic lattice systems in D=1 and D=2 spatial dimensions. A conceptual overview of the steps involved in momentum-space RG is provided and contrasted against the equivalent steps in the real-space setting. The real-space RG flow, as generated by ER, is compared against the exact results from momentum-space RG, including an investigation of a critical fixed point and the effect of relevant and irrelevant perturbations.