Exact Diagonalization of $\mathrm{SU}(N)$ Fermi-Hubbard Models

Thomas Botzung; Pierre Nataf

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arXiv · 2309.09965

Exact Diagonalization of $\mathrm{SU}(N)$ Fermi-Hubbard Models

Thomas Botzung·Pierre Nataf

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Abstract

We show how to perform exact diagonalizations of $\mathrm{SU}(N)$ Fermi-Hubbard models on $L$-site clusters separately in each irreducible representation ({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 semistandard Young tableaux} (or, equivalently the Gelfand-Tsetlin patterns) corresponding to the targeted irrep. As an application of this color factorization, we study the robustness of some $\mathrm{SU}(N)$ phases predicted in the Heisenberg limit upon decreasing the on-site interaction $U$ 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 intermediate $U$ for $N=4$ at filling $1/4$ on the triangular lattice.

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Thomas Botzung, Pierre Nataf. 2023-09-18. Exact Diagonalization of $\mathrm{SU}(N)$ Fermi-Hubbard Models. https://arxiv.org/abs/2309.09965

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