We present a method for the exact diagonalization of the $\mathrm{SU}(N)$ Heisenberg interaction Hamiltonian using Young tableaus to work directly in each irreducible representation of the global $\mathrm{SU}(N)$ group. This generalized scheme is applicable to chains consisting of several particles per site, with any $\mathrm{SU}(N)$ symmetry at each site. Extending some of the key results of substitutional analysis, we demonstrate how basis states can be efficiently constructed for the relevant $\mathrm{SU}(N)$ subsector, which, especially with increasing values of $N$ or numbers of sites, has a much smaller dimension than the full Hilbert space. This allows us to analyze systems of larger sizes than can be handled by existing techniques. We apply this method to investigate the presence of edge states in $\mathrm{SU}(N)$ Heisenberg and Affleck-Kennedy-Lieb-Tasaki Hamiltonians.We present a method for the exact diagonalization of the $\mathrm{SU}(N)$ Heisenberg interaction Hamiltonian using Young tableaus to work directly in each irreducible representation of the global $\mathrm{SU}(N)$ group. This generalized scheme is applicable to chains consisting of several particles per site, with any $\mathrm{SU}(N)$ symmetry at each site. Extending some of the key results of substitutional analysis, we demonstrate how basis states can be efficiently constructed for the relevant $\mathrm{SU}(N)$ subsector, which, especially with increasing values of $N$ or numbers of sites, has a much smaller dimension than the full Hilbert space. This allows us to analyze systems of larger sizes than can be handled by existing techniques. We apply this method to investigate the presence of edge states in $\mathrm{SU}(N)$ Heisenberg and Affleck-Kennedy-Lieb-Tasaki Hamiltonians.

arXiv:1706.05009Physical review. B./Physical review. BSep 28, 201718 citations

李代数相关的时间演化问题SU（2）和Heisenberg—...

肖青, 孙昌璞

东北师大学报：自然科学版Jan 1, 19910 citations

We present a method for the exact diagonalization of the

\mathrm{SU}(N)

Heisenberg interaction Hamiltonian using Young tableaus to work directly in each irreducible representation of the global

\mathrm{SU}(N)

group. This generalized scheme is applicable to chains consisting of several particles per site, with any

\mathrm{SU}(N)

symmetry at each site. Extending some of the key results of substitutional analysis, we demonstrate how basis states can be efficiently constructed for the relevant

\mathrm{SU}(N)

subsector, which, especially with increasing values of

N

or numbers of sites, has a much smaller dimension than the full Hilbert space. This allows us to analyze systems of larger sizes than can be handled by existing techniques. We apply this method to investigate the presence of edge states in

\mathrm{SU}(N)

Heisenberg and Affleck-Kennedy-Lieb-Tasaki Hamiltonians.