Fig. 7: Exact and estimated eigenvalues versus field value, for the VQSE entanglement spectroscopy implementations.
The input state ρ is given as the reduced state of 4 neighboring qubits from the ground state of (19). Top and bottom rows correspond to ferromagnetic and antiferromagnetic couplings, respectively. Dashed curves represent the exact three largest eigenvalues of ρ, while plot markers indicate the VQSE estimated eigenvalues. In a and c we see that VQSE can accurately estimate the eigenvalues. In b and d we plot 1 − λ1, and the y axis is on a log scale. Here we see that the quantum critical factorization points are detected at h/Jx ≈ 0.76 and h/Jx ≈ 1.43 in (b) and (d), respectively, since at those points we have \({\widetilde{\lambda }}_{1}\approx 1\), and \({\widetilde{\lambda }}_{2},{\widetilde{\lambda }}_{3}\approx 0\).
