Chebyshev expansion of spectral functions using restricted Boltzmann machines

Calculating the spectral function of two dimensional systems is arguably one most pressing challenges in modern computational condensed matter physics. While efficient techniques are available lower dimensions, present insurmountable hurdles, ranging from sign problem quantum Monte Carlo (MC), to entanglement area law tensor network based methods. We hereby a variational approach on Chebyshev expansion and neural representation for wave functions. The moments obtained by recursively applying Hamiltonian projecting space states using modified natural gradient descent method. compare this with approximation which uses Krylov subspace constructed "Chebyshev wave-functions". results one-dimensional two-dimensional Heisenberg model square lattice, those other methods literature.