Fig. 5: Effective Hamiltonian \({\tilde{\boldsymbol{H}}}_{{\mathbf{t}}}\) by multienergy cutoff. | Nature Communications

Fig. 5: Effective Hamiltonian \({\tilde{\boldsymbol{H}}}_{{\mathbf{t}}}\) by multienergy cutoff.

From: Area law of noncritical ground states in 1D long-range interacting systems

Fig. 5

In each of the internal Hamiltonians \(\{h_{s}\}_{s\,=\,0}^{q\,+\,1}\), we perform the energy cutoff up to the energy τs = Es,0 + τ. Here, \(\{{E}_{s,j},|{E}_{s,j}\rangle \}\) are the energy eigenvalues and the corresponding eigenstates of hs, respectively. The internal Hamiltonians hs and \({\tilde{h}}_{s}\) have the same eigenstates \(\{|{E}_{s,j}\rangle \}\) and the same eigenvalues (i.e., \({E}_{s,j}\,=\,{\tilde{E}}_{s,j}\)), as long as Es,j ≤ τs, above which the eigenvalues differ from each other.

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