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Generalizing the quantum sine-Gordon and sausage models, we construct exact S-matrices for higher spin representations with quantum U_q(su(2)) symmetry, which satisfy unitarity, crossing-symmetry, and the Yang-Baxter equations with minimality assumption, i.e. without any unnecessary CDD factor. The deformation parameter q is related to a coupling constant. Based on these S-matrices, we derive the thermodynamic Bethe ansatz equations for q a root of unity in terms of a universal kernel where the nodes are connected by graphs of non-Dynkin type. We solve these equations numerically to find out Hagedorn-like singularities in the free energies at some critical scales and find a universality in the critical exponents, all near 0.5 for different values of the spin and the coupling constant., Comment: 28 pages, 9 figures; Rephrasing and additional comments and a reference added; To appear in Journal of High Energy Physics

We introduce the notion of $su(2)$ spin-$s$ Dicke states, which are higher-spin generalizations of usual (spin-1/2) Dicke states. These multi-qudit states can be expressed as superpositions of $su(2s+1)$ qudit Dicke states. They satisfy a recursion formula, which we use to formulate an efficient quantum circuit for their preparation, whose size scales as $sk(2sn-k)$, where $n$ is the number of qudits and $k$ is the number of times the total spin-lowering operator is applied to the highest-weight state. The algorithm is deterministic and does not require ancillary qudits., Comment: 23 pages + supplementary material (cirq code), v2: added references and important new formulas (1.7) and (A.13), version accepted in Advanced Quantum Technologies