Entanglement renormalization in fermionic systems

TL;DR

This paper demonstrates that entanglement renormalization, via the MERA framework, effectively describes ground states of fermionic lattice models in one and two dimensions, including at quantum critical points, revealing a link to entanglement boundary law violations.

Contribution

It shows for the first time that MERA can accurately represent ground states in two-dimensional fermionic systems at criticality, connecting ER performance to entanglement properties.

Findings

MERA successfully describes 2D fermionic ground states at criticality.

ER performance correlates with logarithmic boundary law violations.

Reformulation of ER in terms of operators and correlation matrices.

Abstract

We demonstrate, in the context of quadratic fermion lattice models in one and two spatial dimensions, the potential of entanglement renormalization (ER) to define a proper real-space renormalization group transformation. Our results show, for the first time, the validity of the multi-scale entanglement renormalization ansatz (MERA) to describe ground states in two dimensions, even at a quantum critical point. They also unveil a connection between the performance of ER and the logarithmic violations of the boundary law for entanglement in systems with a one-dimensional Fermi surface. ER is recast in the language of creation/annihilation operators and correlation matrices.