Entanglement phase transition and holography on a lattice (online)

Abstract

Height models and random tiling are well-studied objects in classical statistical mechanics and combinatorics that lead to many interesting phenomena, such as arctic curve, limit shape and Kadar-Parisi-Zhang scaling. We introduce quantum dynamics to the classical hexagonal dimer, 6- and 19-vertex models to construct frustration-free Hamiltonians with unique ground state being a superposition of tiling configurations subject to a particular boundary configuration. The local Hilbert space is enlarged with a color degree of freedom to generate long range entanglement that makes area law violation of entanglement entropy possible. The scaling of entanglement entropy between half systems is analysed with the surface tension theory of random surfaces and under a q-deformation that weighs random surfaces in the ground state superposition by the volume below, it undergoes a phase transition from area law to volume scaling. At the critical point, the scaling is L logL due to the so-called "entropic repulsion” of Gaussian free fields conditioned to be positive. An exact holographic tensor network description of the ground state is proposed with one extra dimension perpendicular to the lattice. I will also discuss inhomogeneous deformations to obtain sub-volume intermediate scaling and possible generalisations to higher dimension.