scholarly journals Towards a Complete Classification of Symmetry-Protected Topological Phases for Interacting Fermions in Three Dimensions and a General Group Supercohomology Theory

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Qing-Rui Wang ◽  
Zheng-Cheng Gu
Keyword(s):  
Complete Classification ◽  
Three Dimensions ◽  
Topological Phases ◽  
General Group ◽  
Symmetry Protected

scholarly journals Many-body topological invariants from randomized measurements in synthetic quantum matter

2020 ◽  
Vol 6 (15) ◽  
pp. eaaz3666 ◽  
Author(s):  
Andreas Elben ◽  
Jinlong Yu ◽  
Guanyu Zhu ◽  
Mohammad Hafezi ◽  
Frank Pollmann ◽  
...  
Keyword(s):  
Body Wave ◽  
Complete Classification ◽  
Theoretical Description ◽  
Spin Model ◽  
Topological Invariants ◽  
Topological Phases ◽  
Many Body ◽  
Topological Quantum ◽  
The Many ◽  
Symmetry Protected

Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

scholarly journals Why are fractional charges of orientifolds compatible with Dirac quantization?

2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Yuji Tachikawa ◽  
Kazuya Yonekura
Keyword(s):  
String Theory ◽  
Double Cover ◽  
Topological Phases ◽  
Duality Group ◽  
Dirac Quantization ◽  
Type Iib String Theory ◽  
Symmetry Protected

Orientifold pp-planes with p\le 4p≤4 have fractional Dpp-charges, and therefore appear inconsistent with Dirac quantization with respect to D(6{-}p)(6−p)-branes. We explain in detail how this issue is resolved by taking into account the anomaly of the worldvolume fermions using the \etaη invariants. We also point out relationships to the classification of interacting fermionic symmetry protected topological phases. In an appendix, we point out that the duality group of type IIB string theory is the  pin^++ version of the double cover of GL(2,Z).

scholarly journals Tri- and Tetrahyperbolic Isofrequency Topologies Complete Classification of Bianisotropic Materials

2020 ◽  
Vol 10 (3) ◽  
pp. 763 ◽  
Author(s):  
Maxim Durach ◽  
Robert Williamson ◽  
Morgan Laballe ◽  
Thomas Mulkey
Keyword(s):  
Phase Transitions ◽  
Optical Materials ◽  
Complete Classification ◽  
Topological Phases ◽  
Longitudinal Polarization ◽  
Polarization Impedance ◽  
High K ◽  
All Optical ◽  
Zero Group

We describe novel topological phases of isofrequency k-space surfaces in bianisotropic optical materials—tri- and tetrahyperbolic materials—which are induced by the introduction of chirality. This completes the classification of isofrequency topologies for bianisotropic materials, as we showed that all optical materials belong to one of the following topological classes—tetra-, tri-, bi-, mono-, or nonhyperbolic. We showed that phase transitions between these classes occur in the k-space directions with zero group velocity at high k-vectors. This classification is based on the sets of high-k polaritons (HKPs), supported by materials. We obtained the equation describing these sets and characterized the longitudinal polarization-impedance of HKPs.

scholarly journals Symmetry-enriched phases obtained via pseudo anyon condensation

2014 ◽  
Vol 28 (24) ◽  
pp. 1450172 ◽  
Author(s):  
Ling-Yan Hung ◽  
Yidun Wan
Keyword(s):  
Physical Properties ◽  
Complete Classification ◽  
Topological Phases ◽  
Topological Order ◽  
Edge States ◽  
Symmetric Phase ◽  
Internal Symmetries

We propose a framework to describe topological phases with global internal symmetries. This involves embedding the phase of interest into an intrinsic topological-order. Such an embedding is related to the physics of anyon condensation, although no physical condensation actually occurs here. Crucial physical properties of the symmetric phase, such as edge states and global charges of anyons are easily recovered from the embedding. The framework naturally reproduces all phases that are currently known in 2+1 d, and potentially provides a complete classification of symmetric topological phases in 2+1 d. We illustrate our idea with simple examples.

scholarly journals Classification of subsystem symmetry-protected topological phases

2018 ◽  
Vol 98 (23) ◽  
Author(s):  
Trithep Devakul ◽  
Dominic J. Williamson ◽  
Yizhi You
Keyword(s):  
Topological Phases ◽  
Symmetry Protected
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