Confinement in the three-state Potts quantum spin chain in extreme ferromagnetic limit

The authors propose a perturbative scheme capable of predicting the energy spectrum in the 2-kink subspace, the analytic structure of the two-kink scattering amplitude, and the low-energy quasiparticle content (two-kink mesons/bubbles and resonances) activated during a quantum quench.

-The systematic analysis of the various cases is detailed, but its level of technicality may appeal primarily to a specialized audience. In the current form, a broader audience may find it difficult to follow all derivations, though the introduction somewhat mitigates this.

-Ref [26] by some of the authors covers closely related physics in the 3-state Potts model with a longitudinal field (aligned or oblique). While the present work indeed goes beyond the semiclassical methods of [26] through a perturbative treatment, it does not produce a qualitative advance in the overall physical picture: in particular, it does not access the baryonic sector.

The authors develop a perturbative approach for the 3-state Potts quantum spin chain in a longitudinal magnetic field, focusing on the regime of small transverse field (“extreme ferromagnetic regime”). The motivation behind this study also comes from confinement phenomena present in this model. Unlike the Ising chain, much more explored, the Potts model gives access to the confinement of baryonic excitations and, with an oblique longitudinal field, to the hybridization of meson/bubble states with unconfined kinks.
The analysis is restricted to the 2-kink sector of low-energy excitations. The first part of the manuscript systematically examines the eigenstates and eigenenergies for several choices of the longitudinal field. The authors then discuss the two-kink scattering matrix as the ratio between transverse and longitudinal field is varied; tracking the motion of poles and zeros provides a consistent explanation of how resonances emerge from two-kink bound states.
The second part investigates the magnetization dynamics following a quantum quench, again for different longitudinal-field configurations. This analysis parallels that of Ref. [26], but is now complemented by the perturbative framework developed earlier in the manuscript. Comparison with iTEBD data is shown in Fig. 5.2; agreement is good only for very small transverse field, g=0.05. For larger g (g=0.2) deviations are visible, although the theory captures well the overall evolution of the magnetization. The authors study the Fourier transform of the time-dependent magnetization and relate the resulting peak structure to the excitations activated by the quench.

Overall, the work is solid and the results are scientifically reliable. The question is whether the manuscript fits the criteria of SciPost Physics or is more appropriate for SciPost Physics Core. The perturbation theory builds on established techniques for closely related models, and much of the underlying physics has already been examined in Ref. [26]. For this reason, in my opinion, the manuscript appears better aligned with the scope of SciPost Physics Core.

-Fig. 2.1 and 2.3: I like the minimal style of the illustration, but clarity should be improved. In Fig. 2.3, in particular, it is visually difficult to discern whether the blue and green states lie at the same energy. I suggest to add in the plots a vertical axes labeled “energies of the vacua/ false vacuum” (or similar) and a horizontal line for reference.

-Sec 3.2: In my opinion, the term “Evolution” in the section title is misleading, since no dynamics is involved. The section concerns the tuning of the parameter v_2 and the resulting changes in the poles and zeros structure of the two-kink scattering matrix.

-Fig. 5.3 and 5.4, the yaxis is logarithmic, but in my opinion this is not visually clear from the plots and may confuse readers. It should be explicitly marked (e.g. “10^x” plot ticks) and/or emphasized in the figure caption.

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