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|Title:||Complete characterization of the ground-space structure of two-body frustration-free Hamiltonians for qubits|
|Citation:||Ji, Z., Wei, Z., Zeng, B. (2011-10-27). Complete characterization of the ground-space structure of two-body frustration-free Hamiltonians for qubits. Physical Review A - Atomic, Molecular, and Optical Physics 84 (4) : -. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevA.84.042338|
|Abstract:||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.|
|Source Title:||Physical Review A - Atomic, Molecular, and Optical Physics|
|Appears in Collections:||Staff Publications|
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