A generalized multi-scale entanglement renormalization ansatz: more accurate conformal data from a critical lattice model

TL;DR

This paper introduces a generalized multi-scale entanglement renormalization ansatz (MERA) with additional disentangling layers, significantly improving the accuracy of conformal data extraction from critical lattice models.

Contribution

It proposes a new variant of MERA with more disentangling layers, enhancing the precision of conformal data extraction from critical quantum systems.

Findings

Improved accuracy in extracting conformal data using the generalized MERA.

Validated the approach on the critical Ising model with Gaussian MERA.

Demonstrated better scaling dimension estimates compared to traditional MERA.

Abstract

The multi-scale entanglement renormalization ansatz (MERA) provides a natural description of the ground state of a quantum critical Hamiltonian on the lattice. From an optimized MERA, one can extract the scaling dimensions of the underlying conformal field theory. However, extracting conformal data from the ascending superoperator derived from MERA seems to have a limited range of accuracy, even after increasing the bond dimension. Here, we propose an alternative ansatz based on an increasing number of disentangling layers. This leads to generalized versions of MERA that improve the extraction of scaling dimensions, as tested in the Gaussian MERA setting for the critical Ising model.