Exact Diagonalization of $\mathrm{SU}(N)$ Fermi-Hubbard Models
Thomas BotzungPierre Nataf
Thomas BotzungPierre Nataf
Sep 2023
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摘要原文
We show how to perform exact diagonalizations of $\mathrm{SU}(N)$ Fermi-Hubbard models on L-sites clusters separately in each irreducible representation ({\it irrep}) of $\mathrm{SU}(N)$. Using the representation theory of the unitary group $\mathrm{U}(L)$, we demonstrate that a convenient orthonormal basis, on which matrix elements of the Hamiltonian are very simple, is given by the set of {\it semi-standard Young tableaux} (or equivalently the Gel'fand-Tsetlin patterns) corresponding to the targeted irrep. \,As an application, we study the robustness of some $\mathrm{SU}(N)$ phases predicted in the Heisenberg limit upon decreasing the on-site interaction on various lattices of size $L \leq 12$ and for $2 \leq N \leq 6$. In particular, we show that a long range color ordered phase emerges for moderate U for N=4 at filling $1/4$ on the triangular lattice.
