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It was proposed in [(https://doi.org/10.1103/PhysRevLett.114.145301){Chen et al., Phys. Rev. Lett. $mathbf{114}$, 145301 (2015)}] that spin-2 chains display an extended critical phase with enhanced SU$(3)$ symmetry. This hypothesis is highly unexpected for a spin-2 system and, as we argue, would imply an unconventional mechanism for symmetry emergence. Yet, the absence of convenient critical points for renormalization group perturbative expansions, allied with the usual difficulty in the convergence of numerical methods in critical or small-gapped phases, renders the verification of this hypothetical SU$(3)$-symmetric phase a non-trivial matter. By tracing parallels with the well-understood phase diagram of spin-1 chains and searching for signatures robust against finite-size effects, we draw criticism on the existence of this phase. We perform non-Abelian density matrix renormalization group studies of multipolar static correlation function, energy spectrum scaling, single-mode approximation, and entanglement spectrum to shed light on the problem. We determine that the hypothetical SU$(3)$ spin-2 phase is, in fact, dominated by ferro-octupolar correlations and also observe a lack of Luttinger-liquid-like behavior in correlation functions that suggests that is perhaps not critical. We further construct an infinite family of spin-$S$ systems with similar ferro-octupolar-dominated quasi-SU$(3)$-like phenomenology; curiously, we note that the spin-3 version of the problem is located in a subspace of exact G$_2$ symmetry, making this a point of interest for search of Fibonacci topological properties in magnetic systems.
We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave
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
The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for
We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit non-ergodic behavior at strong disorder. The analysis is convenien
Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems as well as disordered ones. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow