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Data for paramagnetic and antiferromagnetic solutions on the square lattice Paramagnetic MIT The mit and imt directories contain RAW gRISB ( ) data for the paramagnetic Mott transition, respectively for increasing and decreasing interaction strengths (metal-to-insulator and insulator-to-metal). The related Matlab/Octave script is nonfreeness_para.m . Running it in Matlab/Octave would produce a figure resembling the published one: The main differences lie in the shape of the arrows (which was fine tuned in post-production, for publication) and the transparent line rendered as dashed (as transparencies are not well supported in Octave). AFM ground state The risb_afm and 2gh_afm directories contain RAW data for for the AFM ground state of the model, as found respectively in RISB and gRISB ( ). The related Matlab/Octave script is nonfreeness_afm.m . Running it in Matlab/Octave would produce a figure resembling the published one: N = ghost 2 N = ghost 2
The Octave version of the script does not support the broken x-axis. You may want to adjust the y-range (run e.g. ylim([0,0.04]) in the command line) to better visualize the RISB and gRISB values for the nonfreeness (at the cost of losing sight of the Heisenberg limit, of course). The Heisenberg values for the order parameter and the double occupancy are hard coded in the script, following Phys. Rev. B 66, 024418 (2002), as detailed in the paper. Structure of RAW (g)RISB data All RISB and gRISB calculations contain the following files: ├── 1bdm_1.dat # one-body density matrix for unit-cell site 1 ├── 1bdm_2.dat # one-body density matrix for unit-cell site 2 ├── dens.last # array containing converged values for <n_{i↑}> and <n_{i↓}> ├── docc.last # array containing converged values for <n_{i↑}n_{i↓}> ├── error.SC.convg # self-consistency error (||λ_old - λ_new|| + ||R_old - R_new||) ├── grisb.input # input file for our custom code implementing the gRISB equations ├── k.dat # 2D momenta used to sample the reduced Brillouin zone ├── lambda.fragments.restart # converged value for the λ tensor in gRISB ├── maxdistance.convg # check on gRISB root condition (max(abs(λ-λ_c))) ├── order_parameters.dat # values of the Néel order parameter ├── R.fragments.restart # converged value for the R tensor in gRISB ├── Z_1.convg # converged value for the quasi-particle weight (site 1) └── Z_2.convg # converged value for the quasi-particle weight (site 2) To build our formulation for the local nonfreeness we load the density and double occupancy values from dens.last and docc.last , respectively. Whenever the root condition is violated over a threshold of we discard the point (putting a NaN , which is not displayed in the plots). This never happens in the published data, but a programmatic check is hard-coded in all scripts. 10−3
