Title: Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures

Journal Article · · Physical Review E
 [1];  [2];  [3];  [4]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science & Technology Division
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Science (CNMS); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computational Science and Engineering Division
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science & Technology Division; Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy
  4. Tokyo Univ. of Science, Chiba (Japan). Dept. of Applied Physics
+ Show Author Affiliations

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003)] 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 in this paper, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)] 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.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1435237
Journal Information:
Physical Review E, Journal Name: Physical Review E Journal Issue: 4 Vol. 97; ISSN PLEEE8; ISSN 2470-0045
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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