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

• URL: http://arxiv.org/abs/2305.14231v2
• Date: Tue, 24 Oct 2023 14:53:08 GMT
• Title: Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States
• Authors: Yuchen Guo, Jian-Hao Zhang, Zhen Bi, Shuo Yang
• Abstract summary: We investigate the phase diagram at the boundary of an infinite two-dimensional cluster state subject to bulk measurements. Our results show that the boundary of the system exhibits volume-law entanglement at the measurement angle. 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.
• Score: 20.295517930821084
• License: http://creativecommons.org/licenses/by/4.0/
• 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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