Fig. 4
From: Constructing exact representations of quantum many-body systems with deep neural networks
Imaginary-time evolution with a DBM for 1D spin models. a Expectation value of energy of the transverse-field Ising Hamiltonian in the exact imaginary-time evolution (continuous line) is compared to the stochastic result obtained with a DBM (filled circles) (δτ = 0.01). Empty circles correspond to the approximate RBM evolution scheme, Eq. (15). We consider the critical point (Γl = Vlm), periodic boundary conditions, and N = 20 sites. b Expectation value of the isotropic antiferromagnetic Heisenberg Hamiltonian (AFHM) in the exact imaginary-time evolution (continuous line) is compared to the stochastic result obtained with a DBM (δτ = 0.01) following the 2d–6h construction. We consider periodic boundary conditions, N = 16 sites. The subscript α in DBMα in panels (a, b) specifies a different initial state \(\left| {{\mathrm{\Psi }}_0} \right\rangle\): α = 1 means that the initial state is an RBM state with hidden-unit density M/N = 1, whereas when α = 0 the initial state is the empty-network state (M = 0). All energies are in units of the transverse field (Γl = 1) for the TFIM, and of the exchange (J = 1) for the AFHM
