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

We analyze a class of quantum spin models defined on half-spaces in the$d$-dimensional hypercubic lattice bounded by a hyperplane with inward unitnormal vector $m\in\mathbb{R}^d$. The family of models was previouslyintroduced as the single species Product Vacua with Boundary States (PVBS)model, which is a spin-$1/2$ model with a XXZ-type nearest neighborinteractions depending on parameters $\lambda_j\in (0,\infty)$, one for eachcoordinate direction. For any given values of the parameters, we prove an upperbound for the spectral gap above the unique ground state of these models, whichvanishes for exactly one direction of the normal vector $m$. For all otherchoices of $m$ we derive a positive lower bound of the spectral gap, except forthe case $\lambda_1 =\cdots =\lambda_d=1$, which is known to have gaplessexcitations in the bulk.

Spectral Gap and Edge Excitations of $d$-dimensional PVBS models on half-spaces