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The staircase model: massless flows and hydrodynamics

Mazzoni, M., Pomponio, O., Castro-Alvaredo, O. ORCID: 0000-0003-1876-7341 & Ravanini, F. (2021). The staircase model: massless flows and hydrodynamics. Journal of Physics A: Mathematical and Theoretical, 54(40), 404005. doi: 10.1088/1751-8121/ac2141


The staircase model (SM) is a simple generalization of the sinh-Gordon model, obtained by complexifying the coupling constant. This produces a new theory with many interesting features. Chief among them is the fact that scaling functions such as Zamolodchikov's c-function display 'roaming' behaviour, that is, they visit the vicinity of an infinite number of conformal fixed points, the unitary minimal models of conformal field theory. This rich structure also makes the model an interesting candidate for study using the generalized hydrodynamic approach to integrable quantum field theory (IQFT). By studying hydrodynamic quantities such as the effective velocities of quasiparticles we can develop a more physical picture of interaction in the theory, both at and away from equilibrium. Indeed, we find that in the SM the effective velocity displays monotonicity features not found in any other IQFT. These admit a natural interpretation when investigated in the context of the massless theories known as MAk(+) models, which provide an effective description of massless flows between consecutive unitary minimal models. Consequently, we find that the effective velocity in the SM can be reconstructed by a 'cut and paste' procedure involving the equivalent functions associated to the massless excitations of suitable MAk(+) models. We also investigate the average currents and densities of higher spin conserved quantities in the partitioning protocol.

Publication Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Publisher Keywords: Integrability, Massless Flows, out-of-equilibrium Dynamics, Generalized Hydrodynamics, Bethe Ansatz
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
Text - Accepted Version
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