Topological order and degenerate singular value spectrum in two-dimensional dimerized quantum Heisenberg model

We study the connection between topological order and degeneracy of the singular value spectrum by explicitly solving the two-dimensional dimerized quantum Heisenberg model in the form of the tensor product state ansatz. Based on the ground-state solution, we find nonzero topological entanglement entropy at the frustrated regime. It indicates a possible topological phase. Furthermore, we find that the singular value spectrum associated with each link in the tensor product state is doubly degenerate only in this phase. Degeneracy of the singular value spectrum is robust against various types of perturbations, in accordance with our expectation for topological order. Our results support the connection among topological order, long-range entanglement, and the dominant degenerate singular values. In the context of the tensor product state ansatz, the numerical evaluation of the singular value spectrum costs far less computation power than that for topological entanglement entropy. Our results provide a more viable way to numerically identify the topological order for the generic frustrated systems.