Entanglement renormalization, scale invariance, and quantum criticality

TL;DR

This paper explores how entanglement renormalization techniques, specifically MERA, can accurately approximate critical ground states of lattice models, revealing a deep connection with conformal field theory and enabling extraction of conformal data.

Contribution

It demonstrates a method to compute critical ground states and conformal data using MERA, linking lattice models with conformal field theory in a precise manner.

Findings

MERA provides accurate approximations of critical ground states.

A connection between MERA and conformal field theory is established.

Conformal data can be extracted from lattice models using this approach.

Abstract

The use of entanglement renormalization in the presence of scale invariance is investigated. We explain how to compute an accurate approximation of the critical ground state of a lattice model, and how to evaluate local observables, correlators and critical exponents. Our results unveil a precise connection between the multi-scale entanglement renormalization ansatz (MERA) and conformal field theory (CFT). Given a critical Hamiltonian on the lattice, this connection can be exploited to extract most of the conformal data of the CFT that describes the model in the continuum limit.