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

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.

28 pages, 15 figures; v2 add references and two data points of topological entanglement entropy for 4 by 4 block; v3 text polishing, final for PRB

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Cited by in corpus (15)

• Quantum entanglement in condensed matter systems
• Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons
• Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Refined Holographic Entanglement Entropy for the AdS Solitons and AdS black Holes
• Entanglement Spectra of Heisenberg Ladders of higher Spin
• Symmetry Protected Quantum State Renormalization
• Topological Phases of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain with Frustrated Next-Nearest-Neighbour Interaction
• Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers
• On integrable matrix product operators with bond dimension $D=4$
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• A useful way to obtain the central charge of entanglement Hamiltonian -- Nested entanglement entropy
• Quantum to classical transition in the ground state of a spin-$S$ quantum antiferromagnet