Topological Order and Degenerate Singular Value Spectrum in Two-Dimensional Dimerized Quantum Heisenberg Model

TL;DR

This paper demonstrates that in a two-dimensional dimerized quantum Heisenberg model, the degeneracy of the singular value spectrum correlates with topological order, offering a computationally efficient method to identify topological phases.

Contribution

It establishes a robust link between singular value spectrum degeneracy and topological order, providing a practical approach for detecting topological phases in frustrated quantum systems.

Findings

Non-zero topological entanglement entropy in the frustrated regime

Degenerate singular value spectrum only in the topological phase

Degeneracy remains stable under various perturbations

Abstract

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 tensor product state ansatz. Based on the ground state solution, we find non-zero 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 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 tensor product state ansatz, the numerical evaluation of singular value spectrum costs far less computation power than the one for topological entanglement entropy. Our results provide a more viable way to numerically identify the topological order for the generic frustrated systems.