Quantum states far from the energy eigenstates of any local Hamiltonian.
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.
Haselgrove
Henry L
HL
School of Physical Sciences, The University of Queensland, Queensland 4072, Australia. hlh@physics.uq.edu.au
Nielsen
Michael A
MA
Osborne
Tobias J
TJ