Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface
نویسندگان
چکیده
منابع مشابه
Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface
The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and...
متن کاملNumerical detection of symmetry enriched topological phases with space group symmetry
Topologically ordered phases of matter, in particular so-called symmetry enriched topological (SET) phases, can exhibit quantum number fractionalization in the presence of global symmetry. In Z2 topologically ordered states in two dimensions, fundamental translations Tx and Ty acting on anyons can either commute or anticommute. This property, crystal momentum fractionalization, can be seen in a...
متن کاملFermionic Symmetry Protected Topological Phases and Cobordisms
It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with Z2 symmetry, where Z2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimensionD ≤ 3 and also predicts that ...
متن کاملSymmetry fractionalization in two dimensional topological phases
Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D topological system can transform under symmetry in a fractional way. For example in fractional quantum Hall systems, excitations can carry fractional charges while the electrons making up the system have charge one. An important question is to understand what symmetry fractionalization (SF) patterns are poss...
متن کاملSymmetry Protected Topological phases of Quantum Matter
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting many particle systems, known as Symmetry Protected Topological (SPT) phases. In common with the topological band insulators these states have a bulk gap and no...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review X
سال: 2016
ISSN: 2160-3308
DOI: 10.1103/physrevx.6.041068