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Everything about Exact diagonalization

Numerical technique for solving quantum Hamiltonians

Exact diagonalization (ED) is a numerical technique used in physics to determine the eigenstates and energy eigenvalues of a quantum Hamiltonian. In this technique, a Hamiltonian for a discrete, finite system is expressed in matrix form and diagonalized using a computer. Exact diagonalization is only feasible for systems with few degrees of freedom, due to the exponential growth of the Hilbert space dimension with the size of the quantum system. It is frequently employed to study lattice models, including the Hubbard model, Ising model, Heisenberg model, t-J model, and SYK model. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Exact diagonalizationA 5-minute orientation
  2. Skim a recent paper: Chemistry beyond the scale of exact diagonalization on a quantum-centric supercomputerInfluential work since 2022
  3. Pick up a classic book: Timber-measure by a line of more ease, dispatch and exactness, then any other way now in use, by a double scaleThe most-reprinted book on the subject
  4. Read the landmark paper: Exact Diagonalization Methods for Quantum SystemsCited 151 times
  5. Go sideways: Aubry–André modelA closely related topic
  6. Go sideways: Binder parameterA closely related topic

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🗂️ The subject at a glance

  1. Expectation values from exact diagonalization
  2. Memory requirements
  3. Comparison with other techniques
  4. Applications
  5. Implementations
  6. Generalizations

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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