2021/03/16 by Douglas Hendry, Hongwei Chen, Phillip Weinberg +2
Mathematics · Physics and Astronomy · #Applied mathematics #Artificial neural network #Boltzmann machine #Chebyshev filter #Chebyshev nodes #Chebyshev polynomials #Computer science #Gradient descent #Hamiltonian (control theory) #Mathematical analysis #Mathematical optimization #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Spectral method #Statistical physics #Subspace topology #Theoretical and Computational Physics #Variational Monte Carlo #Wave function #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.104.205130
8 pages, 5 figs
openalex publication_date 2021/03/16 · arxiv created 2021/05/20 · openalex created_date 2021/12/06 · arxiv updated 2021/12/08 · openalex updated_date 2026/08/06
Calculating the spectral function of two dimensional systems is arguably one of the most pressing challenges in modern computational condensed matter physics. While efficient techniques are available in lower dimensions, two dimensional systems present insurmountable hurdles, ranging from the sign problem in quantum Monte Carlo (MC), to the entanglement area law in tensor network based methods. We hereby present a variational approach based on a Chebyshev expansion of the spectral function and a neural network representation for the wave functions. The Chebyshev moments are obtained by recursively applying the Hamiltonian and projecting on the space of variational states using a modified natural gradient descent method. We compare this approach with a modified approximation of the spectral function which uses a Krylov subspace constructed from the "Chebyshev wave-functions". We present results for the one-dimensional and two-dimensional Heisenberg model on the square lattice, and compare to those obtained by other methods in the literature.