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arXiv · 1705.09491

Divide and conquer method for proving gaps of frustration free Hamiltonians

Michael J. Kastoryano·Angelo Lucia
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Abstract

Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem. For the case of finite-range, frustration free Hamiltonians on a spin lattice of arbitrary dimension, we show that a property of the ground state space is sufficient to obtain such a bound. We furthermore show that such a condition is necessary and equivalent to a constant spectral gap. Thanks to this equivalence, we can prove that for gapless models in any dimension, the spectral gap on regions of diameter $n$ is at most $o\left(\frac{\log(n)^{2+\epsilon}}{n}\right)$ for any positive $\epsilon$.

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Michael J. Kastoryano, Angelo Lucia. 2017-05-26. Divide and conquer method for proving gaps of frustration free Hamiltonians. https://doi.org/10.1088/1742-5468/aaa793

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