2000/04/11 by Anthony Hams, Hans De Raedt · 9 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Theoretical and Computational Physics #physics.comp-ph #physics.data-an #quant-ph
paper · pdf · doi:10.1103/physreve.62.4365
published as Phys. Rev. E62 4365-4377 (2000) · 24 pages, 24 figures
arxiv created 2000/04/11 · openalex publication_date 2000/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A theoretical analysis is given of the equation of motion method, due to Alben et al. [Phys. Rev. B 12, 4090 (1975)], to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind encountered in quantum physics the memory and CPU requirements of this method scale linearly with the dimension of the matrix. We derive a rigorous estimate of the statistical error, supporting earlier observations that the computational efficiency of this approach increases with the matrix size. We use this method and an imaginary-time version of it to compute the energy and specific heat of three different, exactly solvable, spin-1/2 models, and compare with the exact results to study the dependence of the statistical errors on sample and matrix size.