"Quantum tiling and holography on a lattice"
Zhao Zhang , SISSA
[Host: Israel Klich]
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, and six-vertex model to construct frustration-free Hamiltonians with unique ground state being a superposition of tiling configurations subject to a particular boundary configuration. An internal degree of freedom of color is further introduced 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 give with one extra dimension perpendicular to the lattice. We also discuss an alternative realisation with six-vertex model, inhomogeneous deformation to obtain sub-volume intermediate scaling, and possible generalisations to higher dimension.
Condensed Matter Seminar
Thursday, November 10, 2022
Monroe Hall, Room 124
Note special room.
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