Entanglement entropy by tensor renormalization group approach

TL;DR

This paper introduces a tensor renormalization group method to calculate entanglement entropy in 1D quantum systems, accurately reproducing theoretical central charge values.

Contribution

It applies HOTRG to compute entanglement entropy from tensor networks, providing a new numerical approach for quantum many-body systems.

Findings

Accurately computes entanglement entropy in the quantum Ising model.

Obtains the central charge as 0.49997(8), matching the theoretical value 1/2.

Demonstrates the method's effectiveness for arbitrary subsystem sizes.

Abstract

We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a $1 + 1$-dimensional tensor network, which is analogous to the tensor network representation of the partition function. The HOTRG method is used to approximate the reduced density matrix for arbitrary subsystem sizes, from which we obtain the entanglement entropy. We test our method in the quantum Ising model and obtain the entanglement entropy of the ground state by taking the size of time direction to infinity. The central charge $c$ is obtained as $c = 0.49997(8)$ for a bond dimension $D=96$, which agrees with the theoretical value $c=1/2$ within the error.