English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study 't Hooft anomalies of global symmetries in 1+1d lattice Hamiltoniansystems. We consider anomalies in internal and lattice translation symmetries.We derive a microscopic formula for the "anomaly cocycle" using topologicaldefects implementing twisted boundary conditions. The anomaly takes value inthe cohomology group $H^3(G,U(1)) \times H^2(G,U(1))$. The first factorcaptures the anomaly in the internal symmetry group $G$, and the second factorcorresponds to a generalized Lieb-Schultz-Mattis anomaly involving $G$ andlattice translation. We present a systematic procedure to gauge internalsymmetries (that may not act on-site) on the lattice. We show that the anomalycocycle is the obstruction to gauging the internal symmetry while preservingthe lattice translation symmetry. As an application, we construct anomaly-freechiral lattice gauge theories. We demonstrate a one-to-one correspondencebetween (locality-preserving) symmetry operators and topological defects, whichis essential for the results we prove. We also discuss the generalization tofermionic theories. Finally, we construct non-invertible lattice translationsymmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries