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Quantum colored lozenge tiling and entanglement phase transition

Zhao ZhangIsrael Klich
Oct 2022
摘要
While volume violation of area law has been exhibited in several quantum spinchains, the construction of a corresponding model in higher dimensions, withisotropic terms, has been an open problem. Here we construct a 2Dfrustration-free Hamiltonian with maximal violation of the area law. We do soby building a quantum model of random surfaces with color degree of freedomthat can be viewed as a collection of colored Dyck paths. The Hamiltonian maybe viewed as a 2D generalization of the Fredkin spin chain. Its action is shownto be ergodic within the Hilbert subspace of zero fixed Dirichlet boundarycondition and positive height function in the bulk and exhibits anon-degenerate ground state. Its entanglement entropy between subsystemsexhibits an entanglement phase transition as the deformation parameter istuned. The area- and volume-law phases are similar to the one-dimensionalmodel, while the critical point scales with the linear size of the system $L$as $L\log L$. Similar models can be built in higher dimensions with even softerarea law violations at the critical point.
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