Fractional disclination charge and discrete shift in the Hofstadter butterfly
In the presence of crystalline symmetries, topological phases of matter acquire a host of
invariants leading to nontrivial quantized responses. Here we study a particular invariant …
invariants leading to nontrivial quantized responses. Here we study a particular invariant …
Quantized Charge Polarization as a Many-Body Invariant in Crystalline Topological States and Hofstadter Butterflies
We show how to define a quantized many-body charge polarization 𝒫→ for (2+ 1) D
topological phases of matter, even in the presence of nonzero Chern number and magnetic …
topological phases of matter, even in the presence of nonzero Chern number and magnetic …
Characterization and classification of interacting ()-dimensional topological crystalline insulators with orientation-preserving wallpaper groups
While free fermion topological crystalline insulators have been largely classified, the
analogous problem in the strongly interacting case has been only partially solved, and the …
analogous problem in the strongly interacting case has been only partially solved, and the …
Complete Crystalline Topological Invariants from Partial Rotations in Invertible Fermionic States and Hofstadter's Butterfly
The theory of topological phases of matter predicts invariants protected only by crystalline
symmetry, yet it has been unclear how to extract these from microscopic calculations in …
symmetry, yet it has been unclear how to extract these from microscopic calculations in …
Fermionic symmetry fractionalization in dimensions
We develop a systematic theory of symmetry fractionalization for fermionic topological
phases of matter in (2+ 1) D with a general fermionic symmetry group G f. In general, G f is a …
phases of matter in (2+ 1) D with a general fermionic symmetry group G f. In general, G f is a …
Anomalies in (2+ 1) D fermionic topological phases and (3+ 1) D path integral state sums for fermionic SPTs
Abstract Given a (2+ 1) D fermionic topological order and a symmetry fractionalization class
for a global symmetry group G, we show how to construct a (3+ 1) D topologically invariant …
for a global symmetry group G, we show how to construct a (3+ 1) D topologically invariant …
Anomaly cascade in ()-dimensional fermionic topological phases
We develop a theory of anomalies of fermionic topological phases of matter in (2+ 1) D with
a general fermionic symmetry group G f. In general, G f can be a nontrivial central extension …
a general fermionic symmetry group G f. In general, G f can be a nontrivial central extension …
(3+ 1)-dimensional path integral state sums on curved U (1) bundles and U (1) anomalies of (2+ 1)-dimensional topological phases
Given the algebraic data characterizing any (2+ 1)-dimensional [(2+ 1) D] bosonic or
fermionic topological order with a global symmetry group G= U (1)⋊ H, we construct a (3+ 1) …
fermionic topological order with a global symmetry group G= U (1)⋊ H, we construct a (3+ 1) …
Band representations in Strongly Correlated Settings: The Kitaev Honeycomb Model
In the study of quantum spin liquids, the Kitaev model plays a pivotal role due to the fact that
its ground state is exactly known as well as the fact that it may be realized in strongly …
its ground state is exactly known as well as the fact that it may be realized in strongly …
Fractionally Quantized Electric Polarization and Discrete Shift of Crystalline Fractional Chern Insulators
Fractional Chern insulators (FCI) with crystalline symmetry possess topological invariants
that fundamentally have no analog in continuum fractional quantum Hall (FQH) states. Here …
that fundamentally have no analog in continuum fractional quantum Hall (FQH) states. Here …