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Supersymmetry and multicriticality in a ladder of constrained fermions
by Natalia Chepiga, Jiří Minář, Kareljan Schoutens
This is not the current version.
Submission summary
As Contributors:  Natalia Chepiga 
Arxiv Link:  https://arxiv.org/abs/2105.04359v2 (pdf) 
Date submitted:  20210512 10:48 
Submitted by:  Chepiga, Natalia 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of the ground states, the nature of which is however generally unknown. Here we resolve this issue by considering a superfrustrated model, which we deform from the supersymetric point. By numerically studying its twoparameter phase diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric point features period4 and period5 density waves which are connected by a floating phase (incommensurate Luttinger liquid) with smoothly varying density. Supersymmetric point emerges as a multicritical point between these three phases. Inside the period4 phase we report a valencebond solid type ground state that persists up to the supersymmetric point. Our numerical data for transitions out of densitywave phases are consistent with the PokrovskyTalapov universality class. Furthermore, our analysis unveiled a period3 phase with a boundary determined by a competition between single and twoparticle instabilities accompanied by a doubling of the wavevector of the density profiles along a line in the phase diagram.
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Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 202174 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2105.04359v2, delivered 20210704, doi: 10.21468/SciPost.Report.3180
Strengths
1systematic study of the phases in a spinless fermion model with a supersymmetric multicritical point
2clear phenomenological picture of the ground and excited states in limiting cases
3criticalities in floating phases
Weaknesses
1The explanation for the algorithm in Appendix A can be improved.
Report
The authors study the phase diagram of a constrained spinless fermion model on a zigzag ladder. The model possesses a supersymmetric point at which the ground state degeneracy is extensive. The perturbation away from the supersymmetric point lifts this massive degeneracy and leads to either gapless or gapped phase, depending on the relative strength of the third and fourth neighbor interactions. An extensive DMRG study reveals that (i) the gapless phase is an incommensurate Luttinger liquid phase described by c=1 CFT and (ii) the transition between the gapless and gapped phases is in the PokrovskyTalapov universality class. In addition, in some limiting cases, the authors give clear phenomenological pictures of the ground states and excited states, which are consistent with what they found numerically. I think the results are interesting, and the paper is written very nicely. Thus, I recommend the manuscript for publication after the authors consider the following comments and suggestions.
 PXP model
In the first paragraph of the Introduction, the authors classified the PXP model as a model with a kinetically constrained hopping. However, the Hamiltonian of the PXP model consists solely of the constrained local spinflip terms and does not have any kinetic term. Thus, I think the corresponding sentence should be rephrased with more careful wording.
 Eq. (7)
It is not easy to understand what this equation means unless one writes down the 1particle Hamiltonian. As far as I understand, N=5 is special in that the 1particle Hamiltonian is written as a 5x5 matrix with all matrix elements 1. I suggest that the authors write down the explicit Hamiltonian just like Eq. (9).
 Eq. (9)
There must be a typo in this equation. I think the (3,3) element of this matrix should be 1. Otherwise, {\bm v}_{\rm GS} below Eq. (9) cannot be a zeroenergy state.
 Criticality at the supersymmetric point
I wonder if the authors can study the nature of the criticality right at the supersymmetric point. I know the massive ground state degeneracy at the point makes the standard stuff like the central charge meaningless. Nevertheless, I still wonder if one can talk about the criticality of the ground state sector by sector. Are there any particular fermion densities N_f/N at which the lowenergy states are not so degenerate, and the standard CFT machinery applies? (This question might be related to the second comment raised by the other referee: are there any chemical potentials for which the standard analysis makes sense?)
 Boundary of the period3 phase
I like the phenomenological argument presented in Sec. 3.3, as it is intuitive and easy to understand. However, I do not quite see how the phase boundaries obtained by that argument are consistent with the actual boundaries obtained numerically. In the current manuscript, the authors just state that they agree with each other. I wonder if the authors can show an enlargement of the phase diagram around the phase boundary of the period3 phase and show the comparison between numerical and phenomenological results, which would be helpful.
 Uniqueness of the ground state(s)
The authors found that the states Eq. (18) are (19) ground states of the model along the line V_3 = V_4 in the period4 phase. I am curious about whether they are the unique ground states or there are some other ground states. Can the authors prove that there are no other ground states by using the PerronFrobenius theorem etc.?
 Appendix A
This appendix is just hard to understand. I have almost no idea about what Figures 12 (a)(e) mean. What does the fusion graph mean? Does the MPO here mean the MPO expression for the Hamiltonian? I would like to suggest that the authors elaborate on them in both the main text and the caption of Fig. 12.
Requested changes
1. First paragraph of Sec. 3.1:
know in the literature ... > known in the literature ...
Anonymous Report 1 on 2021630 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2105.04359v2, delivered 20210630, doi: 10.21468/SciPost.Report.3149
Report
The authors take a starting point a fermion ladder with extensive groundstate degeneracies following from supersymmetry. They perturb the couplings, breaking the supersymmetry and most of the degeneracies, and analyze this model in great depth. Much of the phase diagram is a c=1 incommensuate phase, but the supersymmetric point is a multicritical point separating nearby period4 and period5 ordered phases as one might have guessed. They also find a period3 phase where the density is at its maximum allowed value.
I think this paper is a solid piece of work, coming from an impressively thorough numerical analysis. Although there are no great surprises, it is well worth knowing how these peculiar supersymmetric points fit into a larger picture. I thus support its publication in SciPost.
I have a few comments.
 I wouldn't say (as the authors do in the abstract) that they have "resolved the issue" of extended degeneracies in the supersymmetric models. They've certainly thoroughly understood one particular case, but I'd say the fully 2d cases are still rather mysterious. I expect the answers there to be much subtler.
 Early on, they fix the chemical potential to be U=1 (the supersymmetric value). I appreciated the need to make the problem tractable, but it would nice to know that nothing particularly depends on this choice. So whereas I wouldn't demand any major work, it would be nice to be reassured via a few checks that nothing dramatically changes if this fixing is relaxed a bit.
 The authors state that in the period4 phase there is an exact ground state along a line segment. They give the exact expression for filling exactly 1/4 (and defined a modified model governing the case where the number of sites is even but not a multiple of 4), but don't display anything specific for other cases. Is the ground state really exact in all cases, or just very close? If the former, they should explain why they haven't given the exact ground state, and if the latter, they should explain. I would expect the former, but would just like to know. Also, presumably if $U\ne 1$, they're no longer exact?
Re the second paragraph of the conclusion: while some speculation is allowed, I worry somewhat that if the hardcore constraint is relaxed along with the supersymmetry, the multicriticality will collapse. Doesn't Landau theory suggest that? If it doesn't, it would be really interesting to understand why not. Probably the authors should clarify this (or correct me if I've misunderstood).
 Re the third paragraph of the conclusion: At least as I understand it, the results of Trebst et al are protected by the "topological symmetry" imposed. So whereas another look at these results would be an excellent idea, I wouldn't expect them to change without breaking the symmetry.
 Re the fourth paragraph of the conclusion: by "problems" what do they mean?? Extensive groundstate degeneracy and what else?