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One dimensional SU($n$) chains with the same irreducible representation $mathcal{R}$ at each site are considered. We determine which $mathcal{R}$ admit low-energy mappings to a $text{SU}(n)/[text{U}(1)]^{n-1}$ flag manifold sigma model, and calculate the topological angles for such theories. Generically, these models will have fields with both linear and quadratic dispersion relations; for each $mathcal{R}$, we determine how many fields of each dispersion type there are. Finally, for purely linearly-dispersing theories, we list the irreducible representations that also possess a $mathbb{Z}_n$ symmetry that acts transitively on the $text{SU}(n)/[text{U}(1)]^{n-1}$ fields. Such SU($n$) chains have an t Hooft anomaly in certain cases, allowing for a generalization of Haldanes conjecture to these novel representations. In particular, for even $n$ and for representations whose Young tableaux have two rows, of lengths $p_1$ and $p_2$ satisfying $p_1 ot=p_2$, we predict a gapless ground state when $p_1+p_2$ is coprime with $n$. Otherwise, we predict a gapped ground state that necessarily has spontaneously broken symmetry if $p_1+p_2$ is not a multiple of $n$.
This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar $CP^{n-1}$ and Grassmannian models. They naturally arise in the description of continuum limits of spin chains, and t
We examine topological terms of $(2+1)$d sigma models and their consequences in the light of classifications of invertible quantum field theories utilizing bordism groups. In particular, we study the possible topological terms for the $U(N)/U(1)^N$ f
The DMRG method is applied to integrable models of antiferromagnetic spin chains for fundamental and higher representations of SU(2), SU(3), and SU(4). From the low energy spectrum and the entanglement entropy, we compute the central charge and the
We present a study of the scaling behavior of the R{e}nyi entanglement entropy (REE) in SU($N$) spin chain Hamiltonians, in which all the spins transform under the fundamental representation. These SU($N$) spin chains are known to be quantum critical
We use extensive DMRG calculations to show that a classification of SU(n) spin chains with regard to the existence of spinon confinement and hence a Haldane gap obtained previously for valence bond solid models applies to SU(n) Heisenberg chains as w