BEGIN:VCALENDAR VERSION:2.0 PRODID:Data::ICal 0.22 BEGIN:VEVENT DESCRIPTION:Zhao Zhang \, SISSA\n\n
Height models and ra ndom tiling are well-studied objects in classical statistical mechanics an d combinatorics that lead to many interesting phenomena\, such as arctic c urve\, limit shape and Kadar-Parisi-Zhang scaling. We introduce quantum dy namics to the classical hexagonal dimer\, and six-vertex model to construc t frustration-free Hamiltonians with unique ground state being a superposi tion of tiling configurations subject to a particular boundary configurati on. An internal degree of freedom of color is further introduced to genera te long range entanglement that makes area law violation of entanglement e ntropy 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 superpositi on 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 s o-called "\;entropic repulsion&rdquo\; of Gaussian free fields conditi oned to be positive. An exact holographic tensor network description of th e ground state is give with one extra dimension perpendicular to the latti ce. We also discuss an alternative realisation with six-vertex model\, inh omogeneous deformation to obtain sub-volume intermediate scaling\, and pos sible generalisations to higher dimension.
\n DTSTART:20221110T203000Z LOCATION:Monroe Hall\, Room 124 SUMMARY:Quantum tiling and holography on a lattice END:VEVENT END:VCALENDAR