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Numerical study of the simplest string bit model

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String bit models provide a possible method to formulate a string as a discrete chain of pointlike string bits. When the bit number M is large, a chain behaves as a continuous string. We study the simplest case that has only one bosonic bit and one fermionic bit. The creation and annihilation operators are adjoint representations of the U(N) color group. We show that the supersymmetry reduces the parameter number of a Hamiltonian from 7 to 3 and, at N = infinity, ensures a continuous energy spectrum, which implies the emergence of one spatial dimension. The Hamiltonian H-0 is constructed so that in the large N limit it produces a world sheet spectrum with one Grassmann world sheet field. We concentrate on the numerical study of the model in finite N. For the Hamiltonian H-0, we find that the would-be ground energy states disappear at N = (M - 1)/2 for odd M > N. Our study reveals that the model has stringy behavior: when N is fixed and large enough, the ground energy decreases linearly with respect to M, and the excitation energy is roughly of order M-1. We also verify that a stable system of Hamiltonian +/- H-0 + xi Delta H requires xi >= -/+ 1.

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