Quantum Entanglement of Tensor Networks with Symmetry Projections

Abstract

We investigate the global-symmetry projections applied to the tensor network states from the view point of the entanglement entropy and the mutual information. The projections to the translational invariant space and to the total-$S^z$-zero space give logarithmically increasing mutual information with respect to the system size. In the anti-ferromagnetic $S=1/2$ Heisenberg chain and lattice, the optimized energies become accurate numerically by using variational states of the projected tensor network states, because the projections reflecting symmetries of the ground states generate quantum entanglement.

arXiv comment12 pages, 3 figures, to be published in J. Phys. Soc. Jpn

References in corpus (15)

• Concentrating Partial Entanglement by Local Operations
• Area laws for the entanglement entropy - a review
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• A class of quantum many-body states that can be efficiently simulated
• Criticality, the area law, and the computational power of PEPS
• Classical simulation of quantum many-body systems with a tree tensor network
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Tensor network decompositions in the presence of a global symmetry
• Quantum phase transition in spin-3/2 systems on the hexagonal lattice - optimum ground state approach
• Entanglement renormalization and gauge symmetry
• Symmetry projection schemes for Gaussian Monte Carlo methods
• Stripe Ansatzs from Exactly Solved Models
• Uniform Matrix Product State in the Thermodynamic Limit