Multipartite Entanglement Measures and Quantum Criticality from Matrix and Tensor Product States

TL;DR

This paper investigates how multipartite entanglement measures derived from matrix and tensor product states can effectively identify quantum phase transitions in various one- and two-dimensional systems.

Contribution

It introduces a numerical approach combining iTEBD and TRG to compute entanglement measures that signal quantum criticality, providing insights into their scaling behaviors.

Findings

Entanglement measures show derivative discontinuity at critical points

Method successfully characterizes quantum phase transitions

Scaling behaviors align with quantum state renormalization ideas

Abstract

We compute the multipartite entanglement measures such as the global entanglement of various one- and two-dimensional quantum systems to probe the quantum criticality based on the matrix and tensor product states (MPSs/TPSs). We use infinite time-evolving block decimation (iTEBD) method to find the ground states numerically in the form of MPSs/TPSs, and then evaluate their entanglement measures by the method of tensor renormalization group (TRG). We find these entanglement measures can characterize the quantum phase transitions by their derivative discontinuity right at the critical points in all models considered here. We also comment on the scaling behaviors of the entanglement measures by the ideas of quantum state renormalization group transformations.