Fig. 1: Results for the t − J and t − Jz square lattice with 10 × 4 sites, t/Jz = 3 and open boundaries in x, periodic boundaries in y direction.
From: Neural network approach to quasiparticle dispersions in doped antiferromagnets
a) Quasiparticle dispersion of a single hole for the t − J system obtained with the recurrent neural network (RNN) (blue markers), compared to the matrix product state (MPS) spectral function from ref. 53 with the spectral weight S indicated by the colormap and shown in the inset for k = (0.4π, 0.5π) (gray dashed lines). We average the energy over the last 100 training iterations with the standard deviation denoted by the respective error bars in blue. b Dispersion of the t − Jz system obtained with the RNN, compared to the MPS spectral function and with the same error bars as in a. c Relative errors \(\Delta \epsilon =\frac{{E}_{{{{{{{{\rm{RNN}}}}}}}}}-{E}_{{{{{{{{\rm{DMRG}}}}}}}}}}{| {E}_{{{{{{{{\rm{DMRG}}}}}}}}}| }\) during the training, with hidden dimension dh = 300. The training was restarted after 20000 steps (dashed lines), with an increased number of samples per iteration from 200 to 600 (t − J) or 1000 (t − Jz) in the last restart.
