Entanglement renormalization in two spatial dimensions

TL;DR

This paper introduces a new entanglement renormalization scheme for large 2D quantum lattice systems, enabling efficient analysis of critical phenomena and ground state properties with minimal computational cost.

Contribution

The authors develop and validate a novel entanglement renormalization method that efficiently handles large 2D quantum systems, especially at critical points, with logarithmic or size-independent computational complexity.

Findings

Successfully analyzed the 2D quantum Ising model for various lattice sizes.

Accurately estimated the critical magnetic field and critical exponent beta.

Found the energy gap scales as 1/L at the critical point.

Abstract

We propose and test a scheme for entanglement renormalization capable of addressing large two-dimensional quantum lattice systems. In a translationally invariant system, the cost of simulations grows only as the logarithm of the lattice size; at a quantum critical point, the simulation cost becomes independent of the lattice size and infinite systems can be analysed. We demonstrate the performance of the scheme by investigating the low energy properties of the 2D quantum Ising model on a square lattice of linear size L={6,9,18,54,inf} with periodic boundary conditions. We compute the ground state and evaluate local observables and two-point correlators. We also produce accurate estimates of the critical magnetic field and critical exponent beta. A calculation of the energy gap shows that it scales as 1/L at the critical point.