Supporting data for "Robust spin squeezing from the tower of states of U(1)-symmetric spin Hamiltonians"

Supporting data for "Robust spin squeezing from the tower of states of U(1)-symmetric spin Hamiltonians" (https://link.aps.org/doi/10.1103/PhysRevA.105.022625, https://arxiv.org/abs/2103.07354), by Tommaso Comparin, Fabio Mezzacapo and Tommaso Roscilde. If you use these data in a scientific work, please cite the corresponding article.<br> For additional details, please contact Tommaso Comparin ([e-mail]). This dataset includes tVMC results for several values of the coupling exponent alpha and of the system size N (see file names). Each file includes a set of relevant observables (see file header). These results are directly shown in Figures 1, 3, 7, 9. Further data processing leads to Fig. 4. <br> Details on the variational Ansatz for tVMC<br> - We employ the pair-product Ansatz defined in the main text. In general, there are N*(N-1)/2 independent spin pairs with 4 possible states for each pair, leading to 4*N complex coefficients.<br> - Thanks to translational invariance, we can use coefficients which only depend on the distance between the two spins, reducing the number of independent pairs to N/2 (for a one-dimensional chain with periodic boundary conditions).<br> - We also impose the spin-inversion symmetry for each spin pair, so that configurations like {up,down} and {down,up} have the same coefficient.<br> - Therefore the total number of variational coefficients in our tVMC simulations is equal to N. NOTE:<br> Data are provided without error bars. An analysis of the statistical/systematic errors is included in the folder Errors, for some representative cases.