Guide to Exact Diagonalization Study of Quantum Thermalization

Jung Hoon Jung, Jae Dong Noh

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Exact diagonalization is a powerful numerical method to study isolated quantum many-body systems. This paper provides a review of numerical algorithms to diagonalize the Hamiltonian matrix. Symmetry and the conservation law help us perform the numerical study efficiently. We explain the method to block-diagonalize the Hamiltonian matrix by using particle number conservation, translational symmetry, particle-hole symmetry, and spatial reflection symmetry in the context of the spin-1/2 XXZ model or the hard-core boson model in a one-dimensional lattice. We also explain the method to study the unitary time evolution governed by the Schrödinger equation and to calculate thermodynamic quantities such as the entanglement entropy. As an application, we demonstrate numerical results that support that the eigenstate thermalization hypothesis (ETH) holds in the XXZ model.

Original languageEnglish
Pages (from-to)670-683
Number of pages14
JournalJournal of the Korean Physical Society
Issue number8
StatePublished - 1 Apr 2020


  • Eigenstate thermalization hypothesis
  • Exact diagonalization
  • Quantum thermalization


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