The Staircase Model: Massless Flows and Hydrodynamics

TL;DR

The paper introduces the staircase model, a generalized sinh-Gordon theory, revealing complex roaming behavior and unique hydrodynamic features, including novel effective velocity monotonicity, and connects it to massless flows between minimal models.

Contribution

It presents the staircase model as a new integrable quantum field theory with distinctive roaming and hydrodynamic properties, linking it to massless minimal model flows and developing a novel 'cut and paste' velocity reconstruction method.

Findings

Effective velocity shows unique monotonicity not seen in other IQFTs.

Roaming behavior of the c-function visits multiple conformal fixed points.

Reconstruction of velocities via a 'cut and paste' method using massless excitation functions.

Abstract

The staircase model 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 staircase model 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 $\mathcal{M}A_k^{(+)}$ models, which provide an effective description of massless flows between consecutive unitary minimal models. Remarkably, we find that the effective velocity in the staircase model can be reconstructed by a "cut and paste" procedure involving the equivalent functions associated to the massless excitations of suitable $\mathcal{M}A_k^{(+)}$ models. We also investigate the average currents and densities of higher spin conserved quantities in the partitioning protocol.