DOI: 10.1103/PhysRevB.54.13047

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• Link
• Title: Exact-diagonalization method for correlated-electron models
• Keywords (optional): ED, SU(2) symmetry, Hubbard model
• Reason (optional): This paper describes how to apply SU(2) symmetry on exact diagonalization, the example is Hubbard model at half filling.

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Elaboration on ideas of SU(2) in ED

• According to this lecture,

  It is however very difficult to combine the SU(2) symmetry with the lattice symmetries in a computationally useful way (non-sparse and computationally expensive matrices)

• Note the finer structure of block on SU(N) symmetry. The J conserved block (basis of one irep of SU(N)) can be further decomposed into sub-block of dimension the same as multiplicity instead of the dimension of irep! (This is because Jz conservation U(1) is included in J conservation SU(2))

Useful links on ED

• Nauty, a set of very efficient C language procedures for determining the automorphism group of a vertex-colored graph.

relevant papers on ED technique for SU(2) symmetry

• Exact Diagonalization of Heisenberg SU(N) Models
• Exact diagonalization of Heisenberg SU(N) chains in the fully symmetric and antisymmetric representations