%0 Journal Article
%A Fernández González, C.
%A Schuch, N.
%A Wolf, M.M.
%A Cirac, J.I.
%A Pérez García, David
%T Frustration Free Gapless Hamiltonians for Matrix Product States
%D 2015
%@ 0010-3616
%U https://hdl.handle.net/20.500.14352/33778
%X 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 such uncle Hamiltonian with the same properties in the thermodynamic limit.
%~