(Springer (de la versión publicada), 2015-01-01) Schuch, N.; Wolf, M. M.; Cirac, J. I.; Pérez García, David; Fernández González, Carlos
For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate ground state space (the so-called non-injective case), we construct another 'uncle' Hamiltonian which is also local and frustration free, has the same ground state space, but is gapless, and its spectrum is R+. The construction is obtained by linearly perturbing the matrices building up the state in a random direction, and then taking the limit where the perturbation goes to zero. For MPS where the parent Hamiltonian has a unique ground state (the so-called injective case) we also build s
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