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

Meaningful topological invariants for mixed quantum states are challenging toidentify as there is no unique way to define them, and most choices do notdirectly relate to physical observables. Here, we propose a simple pragmaticapproach to construct topological invariants of mixed states while preserving aconnection to physical observables, by continuously deforming known topologicalinvariants for pure (ground) states. Our approach relies on expectation valuesof many-body operators, with no reference to single-particle (e.g., Bloch)wavefunctions. To illustrate it, we examine extensions to mixed states of$U(1)$ geometric (Berry) phases and their corresponding topological invariant(winding or Chern number). We discuss measurement schemes, and provide adetailed construction of invariants for thermal or more general mixed states ofquantum systems with (at least) $U(1)$ charge-conservation symmetry, such asquantum Hall insulators.

A recipe for topological observables of density matrices