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 have discussed a consistency condition of Berry phases defined by a localgauge twist and spatial symmetries of the many body system. It imposes a nontrivial gap closing condition under the gauge twist in both finite- andinfinite-size systems. It also implies a necessary condition for the gapped andunique ground state. As for the simplest case, it predicts an inevitable gapclosing in the Heisenberg chain of half integer spins. Its relation to theLieb-Schultz-Mattis theorem is discussed based on the symmetries of the twistedHamiltonian. The discussion is also extended to the (approximately) degeneratedmultiplet and fermion cases. It restricts the number of the states in the lowenergy cluster of the spectrum by the filling of the fermions. Constraints bythe reflection symmetry are also discussed.

Degeneracy and Consistency Condition of Berry phases: Gap Closing under the Twist