Geometric entanglement from matrix product state representations

TL;DR

This paper presents an efficient tensor network-based method to compute geometric entanglement in quantum many-body systems, demonstrating its universality and connection to boundary entropy in critical spin chains.

Contribution

It introduces a novel tensor network algorithm for calculating geometric entanglement per site in finite systems, validated on critical quantum spin chains.

Findings

Finite-size correction to geometric entanglement is universal.

Connection established between entanglement correction and Affleck-Ludwig boundary entropy.

Method successfully applied to prototypical critical spin chains.

Abstract

An efficient scheme to compute the geometric entanglement per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on the matrix product state representations. It is systematically tested for three prototypical critical quantum spin chains, which belong to the same Ising universality class. The simulation results lend strong support to the previous claim [Q.-Q. Shi, R. Or\'{u}s, J. O. Fj{\ae}restad, and H.-Q. Zhou, New J. Phys \textbf{12}, 025008 (2010); J.-M. St\'{e}phan, G. Misguich, and F. Alet, Phys. Rev. B \textbf{82}, 180406R (2010)] that the leading finite-size correction to the geometric entanglement per lattice site is universal, with its remarkable connection to the celebrated Affleck-Ludwig boundary entropy corresponding to a conformally invariant boundary condition.