Topological Transitions from Multipartite Entanglement with Tensor Networks: A Procedure for Sharper and Faster Characterization

2014/06/30 by Román Orús, Roman Orus, Tzu-Chieh Wei +3 · 1 citation
Mathematics · Physics and Astronomy · #Combinatorics #Mathematics #Multipartite #Multipartite entanglement #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Squashed entanglement #Symmetry protected topological order #Topological degeneracy #Topological entropy in physics #Topological order #Topological quantum number #Topology (electrical circuits) #Toric code #cond-mat.str-el #hep-lat #quant-ph

paper · pdf · doi:10.1103/physrevlett.113.257202

published as Phys. Rev. Lett. 113, 257202 (2014) · 5 pages, 4 figures, and supplementary material with 10 pages, 14 figures. Revised version, to appear in PRL

arxiv created 2014/11/21 · openalex publication_date 2014/12/19 · arxiv updated 2014/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Topological order in two-dimensional (2D) quantum matter can be determined by the topological contribution to the entanglement Rényi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here, we show how topological phase transitions in 2D systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on projected entangled pair states to compute this quantity for a torus partitioned into cylinders and then use this method to find sharp evidence of topological phase transitions in 2D systems with a string-tension perturbation. When compared to tensor network methods for Rényi entropies, our approach produces almost perfect accuracies close to criticality and, additionally, is orders of magnitude faster. The method can be adapted to deal with any topological state of the system, including minimally entangled ground states. It also allows us to extract the critical exponent of the correlation length and shows that there is no continuous entanglement loss along renormalization group flows in topological phases.

Citations

• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Topological quantum order: Stability under local perturbations
• Negativity and topological order in the toric code
• Entanglement under the renormalization-group transformations on quantum states and in quantum phase transitions
• Quantum circuits for strongly correlated quantum systems
• Entanglement and majorization in(1+1)-dimensional quantum systems
• Detecting Topological Order in a Ground State Wave Function
• Ground State Fidelity from Tensor Network Representations
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Criticality, the area law, and the computational power of PEPS
• Measuring Entanglement Growth in Quench Dynamics of Bosons in an Optical Lattice
• Breakdown of a Topological Phase: Quantum Phase Transition in a Loop Gas Model with Tension
• Valence-bond states for quantum computation
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
• The density-matrix renormalization group in the age of matrix product states
• Fault-tolerant quantum computation by anyons
• Breakdown of a perturbed \boldsymbol\mathbbmZ_N topological phase
• The density-matrix renormalization group
• Half the entanglement in critical systems is distillable from a single specimen

Cited by

• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry