| Abstract: |
| We discuss recent developments on classes of simple quantum models in one-dimension that have surprising properties. These models have a rich combinatorial ground state structure in terms of Motzkin walks and Brownian excursions, have a local interaction, and unique ground states. They are surprising in that they are not describable by conformal field theories in the limit, and have exponentially more amount of entanglement entropy than even quantum critical systems. We introduce these models and present recent work on their spontaneous U(1) symmetry breaking, correlation functions, and new analytical work on their t-deformations. |
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