Please use this identifier to cite or link to this item: https://doi.org/10.1103/PhysRevA.84.042338
Title: Complete characterization of the ground-space structure of two-body frustration-free Hamiltonians for qubits
Authors: Ji, Z.
Wei, Z. 
Zeng, B.
Issue Date: 27-Oct-2011
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
URI: http://scholarbank.nus.edu.sg/handle/10635/112399
ISSN: 10502947
DOI: 10.1103/PhysRevA.84.042338
Appears in Collections:Staff Publications

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