Fernández González, C.Schuch, N.Wolf, M.M.Cirac, J.I.Pérez García, David2023-06-192023-06-192015-010010-361610.1007/s00220-014-2173-zhttps://hdl.handle.net/20.500.14352/33778For 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 such uncle Hamiltonian with the same properties in the thermodynamic limit.engjournal articlehttp://link.springer.com/article/10.1007%2Fs00220-014-2173-zhttp://link.springer.comopen access530.1Spin chainsQuantumFísica matemáticaTeoría de los quanta2210.23 Teoría Cuántica