Quantum Critical Point and Entanglement in a Matrix Product Ground State

TL;DR

This paper investigates the entanglement properties and quantum critical point of a spin-1 model with a Matrix Product ground state, revealing divergence in entanglement length and derivatives at the critical point.

Contribution

It provides a detailed analysis of entanglement measures near the quantum critical point in a spin-1 model with an exact Matrix Product ground state, highlighting the role of multipartite correlations.

Findings

Entanglement length diverges at the critical point

First derivatives of entanglement measures diverge at a=0

Multipartite correlations are involved in the quantum phase transition

Abstract

In this paper, we study the entanglement properties of a spin-1 model the exact ground state of which is given by a Matrix Product state. The model exhibits a critical point transition at a parameter value a=0. The longitudinal and transverse correlation lengths are known to diverge as a tends to zero. We use three different entanglement measures S(i) (the one-site von Neumann entropy), S(i,j) (the two-body entanglement) and G(2,n) (the generalized global entanglement) to determine the entanglement content of the MP ground state as the parameter a is varied. The entanglement length, associated with S(i,j), is found to diverge in the vicinity of the quantum critical point a=0. The first derivative of the entanglement measure E (=S(i), S(i,j)) w.r.t. the parameter a also diverges. The first derivative of G(2,n) w.r.t. a does not diverge as a tends to zero but attains a maximum value at a=0. At the QCP itself all the three entanglement measures become zero. We further show that multipartite correlations are involved in the QPT at a=0.