Entanglement in the pseudogap regime of cuprate superconductors

Dataset

We proide the data for the main results of [F. Bippus et al. Phys. Rev. B. (2025) https://doi.org/10.1103/xk42-b9cx], all references to figures and equations are pointing to this paper

Context and methodology

• We investigate the Quantum Fisher information and quantum variance in the 2D Hubbard model and in Cuprates. With these measures, strong entanglement in the pseudogap regime is observed. 
• We provide the data accompaning our publication to follow the data availability initatives.
• The spin suceptibility data was obtained with ladder-Dynamical Vertex Approximation (DGA), a diagramtic extension of (DMFT) [G. Rohringer et al. Rev. Mod. Phys. 90, 025003 (2018)]

Technical details

After decompression of the "Archiv.zip" file one finds:

• In the paper we investiagate the Hubbbard model with the usual t,t',t'' hopping parameters. We have two different sets of parameters, each set is stored in folder named ("/tp-0.22-tpp0.14" for t'=-0.22, t''=0.14 and "/tp-0.17-tpp0.13" for t'=-0.17 t''=0.13 ). 
• Within each folder different parameters of coulomb repulsion U, filling n and inverse temperature beta are provided. For example for U=1.25, t' = -0.17, t'' = 0.13, beta = 400, n=0.95 the subfolder is named "/chisp_omega-U1.25-tp-0.17-tpp0.13-beta400-ntot0.95". The available data range can be taken from the figures in [F. Bippus et al. Phys. Rev. B. (2025) https://doi.org/10.1103/xk42-b9cx]
• For eachs et of Hubbard model parameters we provide "I_QV.txt" this file includes all post processing results.
  The rows from top to bottom correspond to:
  (1) The quantum variance (eq.2) as presented in Fig.2 and Fig. S5
  (2) The nuber of bosonic matsubara frequency data points provided for the susceptibility (see next bullet point)
  (3) The index of the 0'th bosonic matsubara frequency (Julia convention i.e.: indices starting at 1, see next bullet point)
  (4) The index of the dominant wave vector (Julia convention, see next bullet point)
  (5) For the Ornstein Zernike (OZ) fit (eq.S7) we provide the fit parameter A=1
  (6) OZ parameter \xi
  (7) OZ parameter \lam
  (8) Non relevant parameter =0
  (9) Quantum Variance from OZ with eq.S6
  (10) Quantum Fisher information from OZ presented in Fig.2
  (11) Quantum Variance from OZ with eq.S5 as presented in Fig.2
  (12) Quantum Fisher information from OZ and analytical eq.S14 as presented in Figs.1,2
  (13) Irrelevant parameter
  (14) Quantum Variance from OZ with eq.S5 on an extrapolated frequency box as presented in Fig.2
  (15) Quantum Variance at the AFM wavevector q=(pi,pi) as presented in Fig. S3
• The results above are derived from the raw susceptinbilty data. Here, within each subfolder text files for each Matsubara frequency are provided (number of frequencies given in "I_QV.txt"). The file provides a table where the entries of the different rows are:
  (1) wavevector q_x
  (2) wavevector q_y
  (3) Re(\chi) from DGA
  (4) Im(\chi) from DGA
  (5) Re(\chi) from DMFT
  (6) Im(\chi) from DMFT

Data for the comparison with experiment can be accessed from the cited papers.