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 investigate the physics of one-dimensional symmetry protected topological(SPT) phases protected by symmetries whose symmetry generators exhibit spatialmodulation. We focus in particular on phases protected by symmetries withlinear (i.e., dipolar), quadratic and exponential modulations. We present asimple recipe for constructing modulated SPT models by generalizing the conceptof decorated domain walls to spatially modulated symmetry defects, and developseveral tools for characterizing and classifying modulated SPT phases. Asalient feature of modulated symmetries is that they are generically onlypresent for open chains, and are broken upon the imposition of periodicboundary conditions. Nevertheless, we show that SPT order is present even withperiodic boundary conditions, a phenomenon we understand within the context ofan object we dub a ``bundle symmetry''. In addition, we show that modulated SPTphases can avoid a certain no-go theorem, leading to an unusual algebraicstructure in their matrix product state descriptions.

Topological quantum chains protected by dipolar and other modulated symmetries