Exact Diagonalization of Heisenberg SU(N) models

Abstract

Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labelled by the set of {\it standard Young tableaux} in which the matrix of the Heisenberg SU(N) model (the quantum permutation of N-color objects) takes an explicit and extremely simple form. Since the relative dimension of the full Hilbert space to that of the singlet space on $n$ sites increases very fast with N, this formulation allows to extend exact diagonalizations of finite clusters to much larger values of N than accessible so far. Using this method, we show that, on the square lattice, there is long-range color order for SU(5), spontaneous dimerization for SU(8), and evidence in favor of a quantum liquid for SU(10).

To be published in Physical Review Letters

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• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Combined use of translational and spin-rotational invariance for spin systems
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Two-leg SU(2n) spin ladder: A low-energy effective field theory approach
• Entanglement properties of the two-dimensional SU(3) AKLT state