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Frustration free gapless Hamiltonians for Matrix Product States
- Source :
- Commun. Math. Phys. 333, 299-333 (2015)
- Publication Year :
- 2012
-
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.<br />Comment: 36 pages, new version with some contents rearranged, and a correction in the injective case
- Subjects :
- Quantum Physics
Condensed Matter - Strongly Correlated Electrons
Subjects
Details
- Database :
- arXiv
- Journal :
- Commun. Math. Phys. 333, 299-333 (2015)
- Publication Type :
- Report
- Accession number :
- edsarx.1210.6613
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00220-014-2173-z