1,305 research outputs found
Theory of interacting topological crystalline insulators
We study the effect of electron interactions in topological crystalline
insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe
material class and host multi-valley Dirac fermion surface states. We find that
interactions reduce the integer classification of noninteracting TCIs in three
dimensions, indexed by the mirror Chern number, to a finite group . In
particular, we explicitly construct a microscopic interaction Hamiltonian to
gap 8 flavors of Dirac fermions on the TCI surface, while preserving the mirror
symmetry. Our construction builds on interacting edge states of symmetry-protected topological (SPT) phases of fermions in two dimensions,
which we classify. Our work reveals a deep connection between 3D topological
phases protected by spatial symmetries and 2D topological phases protected by
internal symmetries.Comment: v2. 10 pages, 3 figures. Added new materials and improved
presentatio
Linguistics
Contains report on one research project.National Institute of Mental Health (Grant 1 P01 MH-13390-03
Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy
states from a lattice model cannot be a trivial symmetric insulator if the
filling per unit cell is not integral and if the lattice translation symmetry
and particle number conservation are strictly imposed. In this paper, we
compare the one-dimensional gapless states enforced by the LSM theorem and the
boundaries of one-higher dimensional strong symmetry-protected topological
(SPT) phases from the perspective of quantum anomalies. We first note that,
they can be both described by the same low-energy effective field theory with
the same effective symmetry realizations on low-energy modes, wherein
non-on-site lattice translation symmetry is encoded as if it is a local
symmetry. In spite of the identical form of the low-energy effective field
theories, we show that the quantum anomalies of the theories play different
roles in the two systems. In particular, We find that the chiral anomaly is
equivalent to the LSM theorem, whereas there is another anomaly, which is not
related to the LSM theorem but is intrinsic to the SPT states. As an
application, we extend the conventional LSM theorem to multiple-charge
multiple-species problems and construct several exotic symmetric insulators. We
also find that the (3+1)d chiral anomaly provides only the perturbative
stability of the gapless-ness local in the parameter space.Comment: 14 + 3 pages, 1 figure. (The first two authors contributed equally to
the work.
Gapping as Constituent Coordination
A number of coordinate constructions in natural languages conjoin sequences which do not appear to correspond to syntactic constituents in the traditional sense. One striking instance of the phenomenon is afforded by the gapping construction of English, of which the following sentence is a simple example: (1) Harry eats beans, and Fred, potatoes Since all theories agree that coordination must in fact be an operation upon constituents, most of them have dealt with the apparent paradox presented by such constructions by supposing that such sequences as the right conjunct in the above example, Fred, potatoes, should be treated in the grammar as traditional constituents, of type S, but with pieces missing or deleted
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