Geometric entanglement from matrix product state representations

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. Orús, J. O. Fjærestad, and H.-Q. Zhou, New J. Phys \textbf{12}, 025008 (2010); J.-M. Stéphan, 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.

4+ pages, 3 figures

References in corpus (6)

• DMRG and periodic boundary conditions: a quantum information perspective
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Universal geometric entanglement close to quantum phase transitions
• Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions
• Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies
• Stiffness in 1D Matrix Product States with periodic boundary conditions

Cited by in corpus (5)

• Characterizing Genuine Multisite Entanglement in Isotropic Spin Lattices
• Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study
• Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction
• Variational determination of multi-qubit geometrical entanglement in NISQ computers
• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models