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arXiv · 1210.6613

Frustration free gapless Hamiltonians for Matrix Product States

Carlos Fernández-González·Norbert Schuch·Michael M. Wolf·J. Ignacio Cirac·David Pérez-García
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Abstract

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 (the so-called non-injective case), we construct another 'uncle' Hamiltonian which is local and frustration free but 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.

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Carlos Fernández-González, Norbert Schuch, Michael M. Wolf, J. Ignacio Cirac, David Pérez-García. 2014-11-24. Frustration free gapless Hamiltonians for Matrix Product States. https://doi.org/10.1007/s00220-014-2173-z

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