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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Motivated by recent experimental progress in the context of ultra-coldmulti-color fermionic atoms in optical lattices, we have developed a method toexactly diagonalize the Heisenberg $SU(N)$ Hamiltonian with several particlesper site living in a fully symmetric or antisymmetric representation of$SU(N)$. The method, based on the use of standard Young tableaux, takesadvantage of the full $SU(N)$ symmetry, allowing one to work directly in eachirreducible representations of the global $SU(N)$ group. Since the $SU(N)$singlet sector is often much smaller than the full Hilbert space, this enablesone to reach much larger system sizes than with conventional exactdiagonalizations. The method is applied to the study of Heisenberg chains inthe symmetric representation with two and three particles per site up to $N=10$and up to 20 sites. For the length scales accessible to this approach, allsystems except the Haldane chain ($SU(2)$ with two particles per site) appearto be gapless, and the central charge and scaling dimensions extracted from theresults are consistent with a critical behaviour in the $SU(N)$ level $k$Wess-Zumino-Witten universality class, where $k$ is the number of particles persite. These results point to the existence of a cross-over between thisuniversality class and the asymptotic low-energy behavior with a gappedspectrum or a critical behavior in the $SU(N)$ level $1$ WZW universalityclass.

Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations