Quantum states far from the energy eigenstates of any local Hamiltonian |
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Authors: | Haselgrove Henry L Nielsen Michael A Osborne Tobias J |
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Institution: | School of Physical Sciences, The University of Queensland, Queensland 4072, Australia. hlh@physics.uq.edu.au |
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Abstract: | What quantum states are possible energy eigenstates of a many-body Hamiltonian? Suppose the Hamiltonian is nontrivial, i.e., not a multiple of the identity, and L local, in the sense of containing interaction terms involving at most L bodies, for some fixed L. We construct quantum states psi which are "far away" from all the eigenstates E of any nontrivial L-local Hamiltonian, in the sense that ||psi-E|| is greater than some constant lower bound, independent of the form of the Hamiltonian. |
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