%0 Journal Article
%J Physical Review APhys. Rev. A
%D 2009
%T Quadratic fermionic interactions yield Hamiltonians with large ground-state energy gaps
%A O’Hara,Michael J.
%A O’Leary,Dianne P.
%X Polynomially large ground-state energy gaps are rare in many-body quantum systems, but useful in quantum information and an interesting feature of the one-dimensional quantum Ising model. We show analytically that the gap is generically polynomially large not just for the quantum Ising model, but for one-, two-, and three-dimensional interaction lattices and Hamiltonians with certain random interactions. We extend the analysis to Hamiltonian evolutions and we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. These results also yield a new perspective on the one-dimensional cluster state.
%B Physical Review APhys. Rev. A
%V 79
%P 032331 - 032331
%8 2009/03/24/
%G eng
%U http://link.aps.org/doi/10.1103/PhysRevA.79.032331
%N 3
%R 10.1103/PhysRevA.79.032331