2015/08/31 by Marc Andrew Valdez, Daniel Jaschke, David L. Vargas +1 · 1 citation
Computer Science · Physics and Astronomy · #Adjacency matrix #Computer science #Eigenvalues and eigenvectors #Ising model #Matrix product state #Mutual information #Opinion Dynamics and Social Influence #Physics #Quantum #Quantum Information and Cryptography #Quantum discord #Quantum entanglement #Quantum information #Quantum many-body systems #Quantum mechanics #Quantum mutual information #Quantum phase transition #Statistical physics #cond-mat.quant-gas #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevlett.119.225301
published as Phys. Rev. Lett. 119, 225301 (2017) · 8 pages, 4 figures, 1 table -- now includes supplemental material
arxiv created 2017/10/15 · openalex publication_date 2017/11/29 · arxiv updated 2017/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the complexity of electroencephalogram or functional magnetic resonance imaging measurements of the brain. Using matrix product state methods, we show that network density, clustering, disparity, and Pearson's correlation obtain the critical point for both quantum Ising and Bose-Hubbard models to a high degree of accuracy in finite-size scaling for three classes of quantum phase transitions, Z2, mean field superfluid to Mott insulator, and a Berzinskii-Kosterlitz-Thouless crossover.