Real-Space Visualization of Quantum Phase Transition by Network Topology
arXiv:1904.04275 · doi:10.1103/PhysRevE.100.012304
Abstract
We demonstrate that with appropriate quantum correlation function, a real-space network model can be constructed to study the phase transitions in quantum systems. For the three-dimensional bosonic system, the single-particle density matrix is adopted to construct the adjacency matrix. We show that the Bose-Einstein condensate transition can be interpreted as the transition into a small-world network, which is accurately captured by the small-world coefficient. For the one-dimensional disordered system, using the electron diffusion operator to build the adjacency matrix, we find that the Anderson localized states create many weakly-linked subgraphs, which significantly reduces the clustering coefficient and lengthens the shortest path. We show that the crossover from delocalized to localized regimes as a function of the disorder strength can be identified as the loss of global connection, which is revealed by the small-world coefficient as well as other independent measures like the robustness, the efficiency, and the algebraic connectivity. Our results suggest that the quantum phase transitions can be visualized in real space and characterized by the network analysis with suitable choices of quantum correlation functions.
arXiv comment7 pages, 6 figures
References in corpus (23)
- Community structure in social and biological networks
- Lethality and centrality in protein networks
- Efficient Behavior of Small-World Networks
- Anderson Transitions
- Self-similar community structure in organisations
- Subgraph Centrality in Complex Networks
- Intensity and coherence of motifs in weighted complex networks
- Bose-Einstein condensation in complex networks
- The Physics of Communicability in Complex Networks
- Statistical-mechanical approach to subgraph centrality in complex networks
- Generalized Bose-Fermi statistics and structural correlations in weighted networks
- Interdisciplinary and physics challenges of Network Theory
- Anomalous Transport in Complex Networks
- Supercondutor-Insulator Transition on Annealed Complex Networks
- Complex Quantum Network Geometries: Evolution and Phase Transitions
- Quantifying Complexity in Quantum Phase Transitions via Mutual Information Complex Networks
- Localization transition on complex networks via spectral statistics
- Localization-Delocalization Transition of Electron States in a Disordered Quantum Small World Network
- Growing Cayley trees described by Fermi distribution
- Phase diagram of the Bose-Hubbard Model on Complex Networks
- Phase transition of light on complex quantum networks
- A complex network description of thermal quantum states in the Ising spin chain
- The Evolution of Hyperedge Cardinalities and Bose-Einstein Condensation in Hypernetworks