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 investigate the phase diagram at the boundary of an infinitetwo-dimensional cluster state subject to bulk measurements using tensor networkmethods. The state is subjected to uniform measurements $M =\cos{\theta}Z+\sin{\theta}X$ on the lower boundary qubits and in all bulkqubits. Our results show that the boundary of the system exhibits volume-lawentanglement at the measurement angle $\theta = \pi/2$ and area-lawentanglement for any $\theta < \pi/2$. Within the area-law phase, a phasetransition occurs at $\theta_c=1.371$. The phase with $\theta\in(\theta_c,\pi/2)$ is characterized by a noninjective matrix product state,which cannot be realized as the unique ground state of a one-dimensional local,gapped Hamiltonian. Instead, it resembles a cat state with spontaneous symmetrybreaking. These findings demonstrate that the phase diagram of the boundary ofa two-dimensional system can be more intricate than that of a standardone-dimensional system.

Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States