Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study

TL;DR

This paper introduces a Numerical Linked Cluster Expansion method to accurately compute bipartite entanglement entropy, including universal corner and line contributions, at a two-dimensional quantum critical point, applicable to various Renyi indices.

Contribution

It develops a novel NLCE approach using rectangular clusters for entanglement entropy calculations in 2D quantum models, enabling precise analysis at criticality.

Findings

Successfully computes universal entanglement entropy contributions at the quantum critical point.

Demonstrates NLCE's capability to handle higher-dimensional critical systems.

Provides results for arbitrary Renyi index alpha, including non-integer values.

Abstract

We develop a method to calculate the bipartite entanglement entropy of quantum models, in the thermodynamic limit, using a Numerical Linked Cluster Expansion (NLCE) involving only rectangular clusters. It is based on exact diagonalization of all n x m rectangular clusters at the interface between entangled subsystems A and B. We use it to obtain the Renyi entanglement entropy of the two-dimensional transverse field Ising model, for arbitrary real Renyi index alpha. Extrapolating these results as a function of the order of the calculation, we obtain universal pieces of the entanglement entropy associated with lines and corners at the quantum critical point. They show NLCE to be one of the few methods capable of accurately calculating universal properties of arbitrary Renyi entropies at higher dimensional critical points.