2018/02/28 by Satoshi Okamoto, Gonzalo Alvarez, Gonzalo A. Álvarez +2
Mathematics · Physics and Astronomy · #Canonical ensemble #Eigenvalues and eigenvectors #Energy (signal processing) #Internal energy #Lanczos resampling #Mathematics #Microcanonical ensemble #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #Thermodynamic limit #cond-mat.str-el
paper · pdf · doi:10.1103/physreve.97.043308
published as Phys. Rev. E 97, 043308 (2018) · 9 pages, 11 figures
arxiv created 2018/04/20 · openalex publication_date 2018/04/20 · arxiv updated 2018/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003)PRBMDO0163-182910.1103/PhysRevB.68.235106] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.010401] to obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S=1/2, we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.