Quantum Entanglement of Tensor Networks with Symmetry Projections

TL;DR

This paper explores how symmetry projections in tensor network states influence entanglement and improve energy accuracy in quantum spin systems, revealing the role of symmetry in quantum entanglement.

Contribution

It demonstrates that symmetry projections in tensor networks generate quantum entanglement and enhance variational energy calculations for ground states of spin chains.

Findings

Symmetry projections increase mutual information logarithmically with system size.

Projected tensor networks accurately approximate ground state energies.

Symmetry-reflecting projections generate significant quantum entanglement.

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.