Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models

TL;DR

This paper uses tensor network methods to analyze entanglement properties in 1D and 2D quantum Ising and XXZ models, revealing how entanglement measures characterize quantum phase transitions and monogamy.

Contribution

It introduces a comprehensive comparison of multiple entanglement measures in 1D and 2D quantum spin models using advanced tensor network techniques.

Findings

Entanglement measures effectively identify quantum phase transitions.

Entanglement monogamy properties vary across models and phases.

Tensor network methods successfully model ground states in 1D and 2D systems.

Abstract

We investigate entanglement properties of infinite 1D and 2D spin-1/2 quantum Ising and XXZ models. Tensor network methods (MPS in 1D and TERG and CTMRG in 2D) are used to model the ground state of the studied models. Different entanglement measures, such as one-site entanglement entropy, one-tangle, concurrence of formation and assistance, negativity and entanglement per bond are calculated and their `characterizing power' to determine quantum phase transitions is compared. A special emphasis is made on the study of entanglement monogamy properties.