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Title:
A New Class of Exactly Solvable Quantum Spin Chain models
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Abstract:
In this talk we will describe a class of exactly solvable models with rich underlying combinatorial structures that violate the widely believed area laws (will be defined in the talk). The ground state is a uniform superposition of Motzkin walks. For spin s=1, we will describe the model, calculate the magnetization, entanglement entropy and 1- and 2- point correlation functions. We will then describe a generalization to integer spin s>1 models with a particular attention paid to the Entanglement of these models. The basic notions of entanglement will be introduced in the talk. Entanglement is a quantum correlation which does not appear classically, and it serves as a resource for quantum technologies such as quantum computing. It was widely believed that the area law could not be violated by more than a logarithmic factor (e.g. based on critical systems and ideas from conformal field theory) in the system’s size. Generalized s>1 exactly solvable models herein have exponentially more entanglement than previously expected, and violate the area law by a square root factor. We use theory of Brownian excursion and ideas from computer science such as fractional matching theory to prove that the energy gap closes as n^{-c}, where c \ge 2, which rules out conformal field theories as the continuum limit of these models.
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