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Abstract: We examine whether it is possible for one-dimensionaltranslationally-invariant Hamiltonians to have ground states with a high degreeof entanglement. We present a family of translationally invariant Hamiltonians{H n} for the infinite chain. The spectral gap of H n is Omega1-polyn.Moreover, for any state in the ground space of H n and any m, there are regionsof size m with entanglement entropy Omegamin{m,n}. A similar constructionyields translationally-invariant Hamiltonians for finite chains that haveunique ground states exhibiting high entanglement. The area law proven byHastings gives a constant upper bound on the entanglement entropy for 1D groundstates that is independent of the size of the region but exponentiallydependent on 1-Delta, where Delta is the spectral gap. This paper provides alower bound, showing a family of Hamiltonians for which the entanglemententropy scales polynomially with 1-Delta. Previously, the best known such boundwas logarithmic in 1-Delta.



Author: Sandy Irani

Source: https://arxiv.org/







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