Fractional disclination charge and discrete shift in the Hofstadter butterfly

Y Zhang, N Manjunath, G Nambiar, M Barkeshli - Physical Review Letters, 2022 - APS
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 …

Quantized Charge Polarization as a Many-Body Invariant in Crystalline Topological States and Hofstadter Butterflies

Y Zhang, N Manjunath, G Nambiar, M Barkeshli - Physical Review X, 2023 - APS
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 …

Characterization and classification of interacting ()-dimensional topological crystalline insulators with orientation-preserving wallpaper groups

N Manjunath, V Calvera, M Barkeshli - Physical Review B, 2024 - APS
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 …

Complete Crystalline Topological Invariants from Partial Rotations in Invertible Fermionic States and Hofstadter's Butterfly

Y Zhang, N Manjunath, R Kobayashi, M Barkeshli - Physical Review Letters, 2023 - APS
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 …

Fermionic symmetry fractionalization in dimensions

D Bulmash, M Barkeshli - Physical Review B, 2022 - APS
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 …

Anomalies in (2+ 1) D fermionic topological phases and (3+ 1) D path integral state sums for fermionic SPTs

S Tata, R Kobayashi, D Bulmash… - … in Mathematical Physics, 2023 - Springer
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 …

Anomaly cascade in ()-dimensional fermionic topological phases

D Bulmash, M Barkeshli - Physical Review B, 2022 - APS
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 …

(3+ 1)-dimensional path integral state sums on curved U (1) bundles and U (1) anomalies of (2+ 1)-dimensional topological phases

R Kobayashi, M Barkeshli - Physical Review B, 2024 - APS
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) …

Band representations in Strongly Correlated Settings: The Kitaev Honeycomb Model

A Fünfhaus, M García-Díez, MG Vergniory… - arxiv preprint arxiv …, 2025 - arxiv.org
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 …

Fractionally Quantized Electric Polarization and Discrete Shift of Crystalline Fractional Chern Insulators

Y Zhang, M Barkeshli - arxiv preprint arxiv:2411.04171, 2024 - arxiv.org
Fractional Chern insulators (FCI) with crystalline symmetry possess topological invariants
that fundamentally have no analog in continuum fractional quantum Hall (FQH) states. Here …