The fate of the spin polaron in the 1D antiferromagnets

1) A new perspective for an old problem.

2) An interesting discussion on quasi-1D materials and the role of interchain coupling.

1) No real new advances (or new results) compared to previous literature.

This paper proposes a new way of attacking a - somehow - old problem, the instability of the quasiparticle weight in the 1D t-J model. The work is based on an exact boson-fermion rewriting of the 1D t-J model proposed by Peter Horsch et al. in the 90's. This provides new interesting perspectives but, I believe, no new findings not reported before. On the other hand, the paper offers interesting discussions on experimental materials (and discusses the effect of the deviation from a strictly 1D system).

I believe this work definitely deserves to be published. However, it may not meet the highest editorial standards of SciPost Physics. Publication in SciPost Physics Core seems more appropriate.

The manuscript under consideration numerically investigates the fate of the spin polaron in a one-dimensional antiferromagnet with a single hole. Specifically, the authors ask if the spin polaron, understood as the bound state of a hole and nearby spins, is formed when a single hole is added to the antiferromagnet. The absence of such a bound state is then interpreted as a manifestation of the spin-charge separation.

The authors find that the answer depends very sensitively on the spin symmetry of the parent spin Hamiltonian - the spin-polaron bound state is present in anisotropic XXZ models but disappears at the isotropic XXX point.

This is entirely consistent with previous studies of the question as described in Ref.33 and also in Phys. Rev. B 76, 115106 (2007).

It is unclear what new the present study adds to the old result. It seems that the differences between the Ising limit of the XXZ model and the isotropic XXX are well understood, both previously and also in the current manuscript, and are primarily due to the gapped nature of spin excitations. It is less clear what goes on in the XY-like (Luttinger) limit where spin excitations are gapless. Yet, the spin-polaron is present (Fig.3b). It would be nice to connect this limit with the previous extensive study of the problem in Ref.41 (which is not presently done).

The authors use their findings to question the standard interpretation of photoemission experiments on quasi-1D materials. They correctly point out that the staggered magnetic field produced by neighboring chains spoils the assumed SU(2) symmetry of a single spin chain and unavoidably stabilizes the spin-polaron. However, this appears to be an “academic” issue because the interchain staggered field appears only below the Neel transition temperature, which is very low for most of the relevant materials, which makes the critique irrelevant for actual experiments.

To conclude, I do not recommend the publication in SciPost unless significant revisions addressing the weaknesses listed above are made.

In this paper, the authors proposed a novel way to compare spin polaron states and single-hole spectral functions between one-dimensional (1D) and two-dimensional (2D) t-J model in the same footing, by introducing an exact slave fermion transformation. Applying the technique to the 1D t-J model, the authors found that a spin-polaron feature emerges once the strength of magnon-magnon interaction $\lambda$ deviate from one that corresponds to the SU(2) t-J model. Numerical results shown in the paper are convincing to reach such a conclusion. Therefore, this paper would be worth being published in SciPost.

In terms of comparison with angle-resolved photoemission (ARPES) data for 1D Mott insulators, the authors emphasized that real materials do not obey the SU(2) t-J model but there are possible interactions that break the symmetry. Therefore, the concept of spin-charge separation is incomplete. This is a correct statement as long as one considers temperatures well below the energy scale of symmetry-breaking interactions.

Concerning the symmetry breaking, Figure 3 demonstrated the change of ARPES spectrum in terms of $\lambda$. In the main text, it was mentioned that "the two spectra seem to be qualitatively similar". However, the distribution of spectral weight seems to be different, for example, the number of stripes running along $k$ direction is deferent: for $\lambda=1$, the number is determined by the size of system, while for $\lambda=0$, the number is roughly determined by the strength of spin-polaron formation. Therefore, it is recommended to make clear which structures are similar each other in the spectra.