Exact diagonalization

Exact diagonalization (ED) is a numerical technique used in <a href="/facts/Physics/a7aH2y08">physics</a> to determine the <a href="/facts/Eigenstates/7jbxd7Dx">eigenstates</a> and energy <a href="/facts/Eigenvalues/8TjEoT8u">eigenvalues</a> of a quantum <a href="/facts/Hamiltonian_(quantum_mechanics)/5XwK2HmD">Hamiltonian</a>. In this technique, a Hamiltonian for a discrete, finite system is expressed in matrix form and <a href="/facts/Matrix_diagonalization/y3MkyTCy">diagonalized</a> using a computer. Exact diagonalization is only feasible for systems with a few tens of particles, due to the exponential growth of the <a href="/facts/Hilbert_space/aDFMh4lV">Hilbert space</a> dimension with the size of the quantum system. It is frequently employed to study lattice models, including the <a href="/facts/Hubbard_model/5pphLNde">Hubbard model</a>, <a href="/facts/Ising_model/lvBpj2h1">Ising model</a>, <a href="/facts/Heisenberg_model_(quantum)/8RPu8n5n">Heisenberg model</a>, <a href="/facts/T-J_model/uFBTjCJy">t-J model</a>, and <a href="/facts/Sachdev-Ye-Kitaev_model/mcgvrva4">SYK model</a>.

Exact diagonalization open-in-new

Exact diagonalization