Fig. 3
From: Constructing exact representations of quantum many-body systems with deep neural networks
Construction of exact DBM representations of Heisenberg models. In this example, a time step of imaginary-time evolution is shown, for the case of the one-dimensional antiferromagnetic Heisenberg model. Dots represent physical degrees of freedom \(\left( {\sigma _i^z} \right)\), squares represent hidden units (hj), triangles represent deep units (dk). The three panels (a–c) represent different possible explicit constructions. In each panel, upper networks are the initial state with arbitrary network form, and the bottom networks are the final states, after application of the propagator. Intermediate steps illustrate how the network is modified, where the relevant modified weights at each step are highlighted in black. In those diagrams, dashed lines indicate that the corresponding weights are set to zero, and dotted lines indicate complex-valued weights. The three panels correspond to the (a) “1 deep, 3 hidden” (1d–3h), (b) “2 deep, 6 hidden” (2d–6h), and (c) “2 deep, 4 hidden” (2d–4h) constructions (see text for a more detailed explanation of the individual steps characteristic of each construction)
