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.

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

References in corpus (5)

• A class of quantum many-body states that can be efficiently simulated
• Criticality, the area law, and the computational power of PEPS
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Entanglement renormalization and gauge symmetry
• Uniform Matrix Product State in the Thermodynamic Limit