The non-Abelian density matrix renormalization group algorithm
By Ian P. McCulloch, M. Gulácsi. 2000
201 citations recorded by the source corpus.
We describe here the extension of the density matrix renormalization group algorithm to the case where the Hamiltonian has a non-Abelian global symmetry group. The block states transform as irreducible representations of the non-Abelian group. Since the representations are multi-dimensional, a single block state in the new representation corresponds to multiple states of the original density matrix renormalization group basis. We demonstrate the usefulness of the construction via the one-dimensional Hubbard model as the symmetry group is enlarged from U(1)×U(1), up to SU(2)×SU(2).
Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/c5dbef5a96041002d7ea1ad898c8527f27927c0a
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In Atomic and Molecular Physics, and Optics
- Norbert Schuch
- Frank Verstraete
- I. Cirac
- David Pérez-García
- Frank Pollmann
- J. Hauschild
- J. Haegeman
- J. Dubail
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “…tensor Ai can be written in terms of Clebsch-Gordan coefficients of irreducible representations of the group G and the variational degrees of freedom can be incorporated by adding multiplicities (McCulloch and Gulácsi, 2002; Sanz et al., 2009b; Singh et al., 2010; Weichselbaum, 2012; White, 1993).”
- Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy) (2018, background): “[13,14,16,17] for the non-abelian case, which requires a change of the computational basis and is much more difficult to implement.”