$Z_Q$ Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices [PDF]
, 2010 Adiabatic $Z_Q$ invariants by quantized Berry phases are defined for gapped electronic systems in $d$-dimensions ($Q=d+1$). This series includes Polyacetylene, Kagome and Pyrochlore lattice respectively for $d=1,2$ and 3.
Creutz M. +5 more
core +2 more sources
Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus
Physical Review X, 2014 We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and ...
Zhong Wang, Shou-Cheng Zhang
doaj +1 more source
Wilson loop invariants from WN conformal blocks
Nuclear Physics B, 2015 Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point ...
Oleg Alekseev, Fábio Novaes
doaj +1 more source
Phase of Topological Lattice with Leaky Guided Mode Resonance
Nanomaterials, 2023 Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material.
Heejin Choi +4 more
doaj +1 more source
Robust topological invariants of topological crystalline phases in the presence of impurities [PDF]
Physical review B, 2019 Topological crystalline phases (TCPs) are topological states protected by spatial symmetries. A broad range of TCPs have been conventionally studied by formulating topological invariants (symmetry indicators) at invariant momenta in the Brillouin zone ...
Ian Mondragon-Shem, T. Hughes
semanticscholar +1 more source
The study of line graphs of subdivision graphs of some rooted product graphs via K-Banhatti indices
International Journal of Mathematics for Industry, 2023 The degree-based topological indices are numerical graph invariants that are used to link a molecule’s structural characteristics to its physical, and chemical characteristics.
K. J. Gowtham, N. Narahari
doaj +1 more source
Topological Invariants for Closed Hypersurfaces [PDF]
Bulletin of the Brazilian Mathematical Society, New Series, 2018 Comment: 6 ...
Icaro Gonçalves, Eduardo Longa
openaire +3 more sources
Machine Learning Topological Invariants with Neural Networks [PDF]
Physical Review Letters, 2017 In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can ...
Pengfei Zhang, Huitao Shen, H. Zhai
semanticscholar +1 more source
Creation of electrical knots and observation of DNA topology
New Journal of Physics, 2021 Knots are fascinating topological structures that have been observed in various contexts, ranging from micro-worlds to macro-systems, and are conjectured to play a fundamental role in their respective fields.
Tian Chen +5 more
doaj +1 more source
Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries [PDF]
Physical review B, 2017 We present a fully many-body formulation of topological invariants for various topological phases of fermions protected by antiunitary symmetry, which does not refer to single particle wave functions. For example, we construct the many-body $\mathbb{Z}_2$
Ken Shiozaki +3 more
semanticscholar +1 more source