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arXiv · 2305.14231

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

Yuchen Guo·Jian-Hao Zhang·Zhen Bi·Shuo Yang
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Abstract

We investigate the phase diagram at the boundary of an infinite two-dimensional cluster state subject to bulk measurements using tensor network methods. The state is subjected to uniform measurements $M = \cos{\theta}Z+\sin{\theta}X$ on the lower boundary qubits and in all bulk qubits. Our results show that the boundary of the system exhibits volume-law entanglement at the measurement angle $\theta = \pi/2$ and area-law entanglement for any $\theta < \pi/2$. Within the area-law phase, a phase transition 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 symmetry breaking. These findings demonstrate that the phase diagram of the boundary of a two-dimensional system can be more intricate than that of a standard one-dimensional system.

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Yuchen Guo, Jian-Hao Zhang, Zhen Bi, Shuo Yang. 2023-05-23. Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States. https://doi.org/10.1103/physrevresearch.5.043069

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