Topological Order and Degenerate Entanglement Spectrum in Two-Dimensional Dimerized Quantum Heisenberg Model
Ching-Yu Huang, Feng-Li Lin
Abstract We study the connection between topological order and degeneracy of the entanglement spectrum by explicitly solving the two-dimensional dimerized quantum Heisenberg model in the form of tensor product state ansatz. By evaluating the topological entanglement entropy, we identify a new phase with topological order in this model, in which the entanglement spectrum is doubly degenerate. Degeneracy of the entanglement 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 of entanglement spectrum. In the context of tensor product state ansatz, the numerical evaluation of entanglement 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.
•Apr 6, 2011•1 citation