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- W2471635648 abstract "We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian $beta-$orthogonal random matrix ensemble. As a corollary there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal." @default.
- W2471635648 created "2016-07-22" @default.
- W2471635648 creator A5056471458 @default.
- W2471635648 date "2017-11-29" @default.
- W2471635648 modified "2023-10-02" @default.
- W2471635648 title "Generic Local Hamiltonians are Gapless" @default.
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- W2471635648 doi "https://doi.org/10.1103/physrevlett.119.220504" @default.
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