The repository contains the data, code and scripts used to produce the figures in the main text and SI.
The main folder of the repository contains MATLAB scripts which can be used to reproduce the various plots in the main text and SI.
In particular:
    - pseudocolor_plot.m can be used to reproduce all pseudo-color-plot panels. To reproduce a given panel call the function pseudocolor_plot with the name of the figure/panel as an argument.
        For example, to reproduce Fig.2 call
	>> pseudocolor_plot('2')
	or for panel b (corresponding to B=8T) of Fig.3 call
	>> pseudocolor_plot('3b')

    - convergence_analysis.m can be used to reproduce all panels displaying the convergence analysis (Fig. S3 to S5). To reproduce a given panel call the function convergence_analysis with the name of the figure/panel as an argument.
        For example, to reproduce panel c of Fig.S5 call
	>> convergence_analysis('S5c')

The additional folders contain the content detailed below.

  - DSF_itensor: an implementation of a 3-site tDMRG algorithm using ITensor (v2) and the various utilities used for obtaining the numerical simulations.
      To compile the program open Makefile and modify line 6 inserting the path to the itensor library (v2) on your machine. Run "make" to compile the program.
      The program Ising_DSF can be called as ./Ising_DSF "name of input file".
      Example of input files can be filed in the following folders under the name "input.txt"

  - fitting scripts: the MATLAB scripts used to fit the parameters of  the model. In particular
    - hy_0_fit contains the scripts used to fit the model parameters for h_y = 0; the main script is fit.m, while the other files are functions called in the fit
    - g_factor contains the scripts used to fit the g-factor; again, the main script is fit.m

  - main_text_data : contains the data (grouped by figure and panel) used to produce the figures in the main text (see below for an explanation on the formats)

  - SI_data: contains the data (grouped by figure and panel) used to produce the figures in the SI

The format of the data in the last 2 folders is detailed below.
Each folder containing the results of tDMRG simulations is composed by the following files:
  -input.txt specifying the parameters for that simulation
    the various parameters are as follows

      N = the number of sites
      T = maximum time evolved (in 1/J units)
      cutoff = \varepsilon (threshold for neglecting singular values)
      Xmax = maximum bond dimension
      dt = Trotter step
      measure_every = measure every "measure_every" Trotter steps
      hx = field in the x direction
      hy = field in the y direction
      hz = field in the z direction
      hz_over_m = J^{zz}_{ic}
      m_tol = the tolerance on the self-consistent computation of the magnetization along z
      misalignment = the fraction of the x and y field that is misaligned in the z direction
        Note that this is 0 in the present work, and was introduced to compare with Ref.[20]
      pairing = \lambda_A in the notation of the paper
      yz = \lambda_yz in the notation of the paper
      hopping = \lambda_S in the notation of the paper
      NNNZZ = \lambda_AF in the notation of the paper

      component = describe the component of the DSF to measure
          1 for xx
          2 for yy
          3 for zz

  - energy.txt containing general information on the tDMRG run. The format is as follows

      number of total tDMRG sweeps to get to the desired final time
      energy of the ground state
      average magnetization along z
      total field in the z direction

  - Tevol_out_re, Tevol_out_im detailing the time evolution of <S^\alpha_j(t_i) S^\alpha(0)>
     where t_i is the time of the i-th measurement.
    The real (imaginary) part of <S^\alpha_j(t_i) S^\alpha(0)> is stored in the i-th row (from the top) and the j-th column of Tevol_out_re (Tevol_out_im)

  -Tevol_out_m storing the evolution of the bond dimension with time
    The bond dimension between site j and j+1 at time t_i is stored in the i-th row (from the top) and the j-th column of Tevol_out_m

  -for the data used in pseudo-color plots, an additional file plot_parameters.txt is present, which is used in the post-processing of the tDMRG data. The format is as follows

    J/\eta
    J
    k_min
    k_max
    omega_min
    omega_max
    omega_cut
    rescaling_factor

    where the momentum interval in the plot is [k_min,k_max] and similarly for omega. If omega_cut>0 the DSF data below frequency omega_cut is multiplied by rescaling_factor as in Fig.2

Finally, we report the experimental data used in Fig.2 and 4.
  - Fig.2: the experimental data points are taken from Fig.3D of Ref.[18]. The data is reported in the files
        kinetic_bound_state.dat  mode2b.dat  mode3.dat	 mode5b.dat
        mode1b.dat		 mode2.dat   mode4b.dat  mode5.dat
        mode1.dat		 mode3b.dat  mode4.dat
    in the folder main_text_data/fig_2/experimental_data,
    in the format [k, E, dE], where k is the momentum component in the c direction, while E and dE are the energy of the mode and the associated uncertainty.

  - The data used in Fig.4 is reported as a high-resolution png file: main_text_data/fig_4/experimental_data/CoNb2O6_INS_2.5T_b_field_whitebg.png
