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.
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.

Details on the variational Ansatz for tVMC
- 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.
- 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).
- We also impose the spin-inversion symmetry for each spin pair, so that configurations like {up,down} and {down,up} have the same coefficient.
- Therefore the total number of variational coefficients in our tVMC simulations is equal to N.

NOTE:
Data are provided without error bars. An analysis of the statistical/systematic errors is included in the folder Errors, for some representative cases.