2025/11/05 by Nicolò Brizio, Brizio, Nicolò, Tommaso Morone +5
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2511.03791
openalex publication_date 2025/11/05 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28
We introduce and study a class of two-dimensional integrable quantum field theories that carry an internal ℤn structure. These models extend factorised scattering beyond the conventional framework, featuring both the usual hierarchy of integer-spin conserved charges and an additional tower of fractional-spin ones. Our construction relies on a reparametrisation of rapidity space that lifts standard scattering amplitudes to a multiplet related by an internal cyclic symmetry. This construction is naturally embedded within a generalised Gibbs ensemble, which provides the natural framework for a consistent graded Thermodynamic Bethe Ansatz. This leads to new Y-systems encoding the graded spectrum. In a special case, these functional relations match those obtained via the ODE/IM correspondence from the monodromy analysis of the quantum cubic oscillator. Even in the simplest models, for one sign of the auxiliary temperature, the finite-volume ground-state energy spectrum undergoes an infinite sequence of level crossings as the coupling strength increases. A preliminary analysis also suggests that these theories exhibit structural connections with cyclic orbifolds. Within this setup, one can consistently include extra CDD factors that realise fractional-spin analogues of the TT deformation. In analytically tractable cases, a Hagedorn-like behaviour is observed for a sign of the flow parameter, and the deformed spectrum develops a finite limiting temperature.