Quantum lozenge tiling and entanglement phase transition

• URL: http://arxiv.org/abs/2210.01098v3
• Date: Tue, 08 Oct 2024 12:46:44 GMT
• Title: Quantum lozenge tiling and entanglement phase transition
• Authors: Zhao Zhang, Israel Klich,
• Abstract summary: We construct a frustration-free Hamiltonian with maximal violation of the area law. It is conjectured that similar models with entanglement phase transitions can be built in higher dimensions.
• Score: 5.201207023965752
• License:
• Abstract: While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, has been an open problem. Here we construct a 2D frustration-free Hamiltonian with maximal violation of the area law. We do so by building a quantum model of random surfaces with color degree of freedom that can be viewed as a collection of colored Dyck paths. The Hamiltonian may be viewed as a 2D generalization of the Fredkin spin chain. It relates all the colored random surface configurations subject to a Dirichlet boundary condition and hard wall constraint from below to one another, and the ground state is therefore a superposition of all such classical states and non-degenerate. Its entanglement entropy between subsystems undergoes a quantum phase transition as the deformation parameter is tuned. The area- and volume-law phases are similar to the one-dimensional model, while the critical point scales with the linear size of the system $L$ as $L\log L$. Further it is conjectured that similar models with entanglement phase transitions can be built in higher dimensions with even softer area law violations at the critical point.

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