A major chall enge of physics is the complexity of many-body systems. While true for cla ssical systems\, the difficulty is exasperated in quantum systems\, due to entanglement between system components and thus the need to keep track of an exponentially large number of parameters. In particular\, this complex ity places a challenge to numerical methods such as quantum Monte Carlo an d tensor networks. Here\, exactly solvable models are of crucial importanc e: \;we use these to test numerical procedures\, to develop intuition \, and as a starting point for approximations.

\n\ nIn this talk\, I will explain our current understanding of a new solvable "\;walk"\; model\, the area deformed Motzkin model. The model show s that entanglement may be more acute than previously thought\, in particu lar\, it features a novel quantum phase transition between a non-entangled phase and extensively entangled &ldquo\;rainbow&rdquo\; phase. Most remar kably\, the model motivated the construction of a new tensor network\, pro viding\, after many years\, the first example for an exact tensor network description of a critical system. Finally\, I will remark on open problems \, and on exciting connections to other fields such as the notion of holog raphy in field theory\, and a famous problem in non-equilibrium statistica l mechanics.

\n DTSTART:20190913T193000Z LOCATION:Physics Building\, Room 204 SUMMARY:Quantum states\, walks\, tiles\, and tensor networks END:VEVENT END:VCALENDAR