2015/10/31 by Kensaku Takai, Kota Ido, Takahiro Misawa +2 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Eigenvalues and eigenvectors #Ground state #Hilbert space #Hubbard model #Imaginary time #Lanczos resampling #Mathematics #Monte Carlo method #Path integral formulation #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum mechanics #Quantum statistical mechanics #Statistical physics #Variational Monte Carlo #cond-mat.mtrl-sci #cond-mat.str-el
paper · pdf · doi:10.7566/jpsj.85.034601
published as JPSJ. 85. 034601 (2016) · 13 pages, 9 figures, plus appendix
arxiv created 2016/01/25 · openalex publication_date 2016/02/18 · arxiv updated 2016/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A new computational method for finite-temperature properties of strongly correlated electrons is proposed by extending the variational Monte Carlo method originally developed for the ground state. The method is based on the path integral in the imaginary-time formulation, starting from the infinite-temperature state that is well approximated by a small number of certain random initial states. Lower temperatures are progressively reached by the imaginary-time evolution. The algorithm follows the framework of the quantum transfer matrix and finite-temperature Lanczos methods, but we extends them to treat much larger system sizes without the negative sign problem by optimizing the truncated Hilbert space on the basis of the time-dependent variational principle (TDVP). This optimization algorithm is equivalent to the stochastic reconfiguration (SR) method that has been frequently used for the ground state to optimally truncate the Hilbert space. The obtained finite-temperature states allow an interpretation based on the thermal pure quantum (TPQ) state instead of the conventional canonical-ensemble average. Our method is tested for the one- and two-dimensional Hubbard models and its accuracy and efficiency are demonstrated.