Complete characterization of the ground-space structure of two-body frustration-free Hamiltonians for qubits

Publication Type:
Journal Article
Citation:
Physical Review A - Atomic, Molecular, and Optical Physics, 2011, 84 (4)
Issue Date:
2011-10-27
Full metadata record
Files in This Item:
Filename Description Size
PhysRevA.84.042338.pdfPublished Version270.08 kB
Adobe PDF
The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is always a ground state that is a product of single- or two-qubit states. However, it remains unclear whether the whole ground space is of any succinct structure. Here, we give a complete characterization of the ground space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a span of tree tensor network states of the same tree structure. This characterization allows us to show that the problem of determining the ground-state degeneracy is as hard as, but no harder than, its classical analog. © 2011 American Physical Society.
Please use this identifier to cite or link to this item: