Two-site entanglement in the two-dimensional Hubbard model

With this data set, we aim to make all data published in [1] Bippus. et. al Two-site entanglement in the two-dimensional Hubbard model (2025) arXiv:2506.09780 publicly available. In this study, the entanglement properties of the 2D Hubbard model in the weak coupling regime are investigated. 

We include three data sets:

Density Matrices

The Density_Matrices.zip includes all density matrices which were obtained with the parquet approximation (pa) and dynamical vertex approximation (dga) as described in [1]. From them all entanglement measures shown in [1] can be computed.

The data is structured as follows:
Density matrices for each set of Hubbard model parameters U,n,mu,beta is provided in a separate directory i.e.: wgamma_u2.0_n1.00000_mu1.00000_beta5.000000_pa_grain1 with _pa, _dga signalling the approximation that has been used and _grain1 is added for data that does not use coarse graining. 
Each directory includes rho_(dx,dy).csv files containing the 16x16 two-site reduced density matrices of two lattice sites separated by distance (dx,dy) in the basis specified in [1].

QMC

The QMC.zip data set includes all quantum Monte Carlos benchmark data used in [1]. All data were obtained with the Algorithms for Lattice Fermions (ALF) library [2]. A detailed description of the output files is provided in [2].

The data is structured as follows:
Each set of considered Hubbard model parameters is provided in a separate directory i.e.: U4.0_n_1.0_beta5.0 with the Rényi Mutual information stored mutual_{}.dat files. For {} = 10, data is shown along the horizontal direction, for {} = 11 data is shown along the diagonal direction, {} = 2D or no addition includes data for all lattice sites in the irreducible wedge.

U0

The U0.zip includes the semi-analytical results for the mutual information in the non-interacting Hubbard model and contains two .dat files of the mutual information at half filling and n=0.8.

[1] Bippus. et. al Two-site entanglement in the two-dimensional Hubbard model (2025) arXiv:2506.09780

[2] Assaad. et. al The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code (2025) 10.21468/SciPostPhysCodeb.1-v2.4