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Title:
Quantum spin chains: Generic Properties and Exactly Solvable Models
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Abstract:
We will discuss the ground states, frustration free condition and the gap of generic local Hamiltonians [1,2]. There is a promising angle of attack to quantify the entanglement of such Hamiltonians that uses a genericity argument from algebraic geometry. This approach naturally motivates the search for specific and highly entangled spin chain models. In recent years, there has been a surge of activities in proposing exactly solvable quantum spin chains with the surprisingly high amount of entanglement entropies (super-logarithmic violations of the area law). We will discuss these models starting from the spin-1 Motzkin spin chain [3], to the super-critical colored-Motzkin Hamiltonian, which gives a \sqrt(n) factor violation of the area law [4], to the very recent proposal of Fredkin Spin Chain [5]. We will then prove that the gap of [5] scales as n^{-c}, where 2\le c \le 13/2 and therefore this model, like [3,4], does not have a relativistic conformal field theory description [6]. Time permitting we might discuss the gap of a deformation of [4] which violates the area law maximally [7].
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