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Weak topological insulating phases of hardcorebosons on the honeycomb lattice
by Amrita Ghosh, Eytan Grosfeld
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Submission summary
Authors (as registered SciPost users):  Amrita Ghosh · Eytan Grosfeld 
Submission information  

Preprint Link:  https://arxiv.org/abs/2010.16126v2 (pdf) 
Date submitted:  20201103 15:20 
Submitted by:  Grosfeld, Eytan 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
We study the phases of hardcorebosons on a twodimensional periodic honeycomb lattice in the presence of an onsite potential with alternating sign along the different ylayers of the lattice. Using quantum Monte Carlo simulations supported by analytical calculations, we identify a weak topological insulator, characterized by a zero Chern number but nonzero Berry phase, which is manifested at either density 1/4 or 3/4, as determined by the potential pattern. Additionally, a chargedensitywave insulator is observed at 1/2filling, whereas the phase diagram at intermediate densities is occupied by a superfluid phase. The weak topological insulator is further shown to be robust against any amount of nearestneighbor repulsion, as well as weak nextnearestneighbor repulsion. The experimental realization of our model is feasible in an optical lattice setup.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2020129 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2010.16126v2, delivered 20201209, doi: 10.21468/SciPost.Report.2269
Report
This manuscript studies a bosonic analogue of weak topological insulating phases on the honeycomb lattice. Specifically the model studied are on a twodimensional periodic honeycomb lattice in the presence of an onsite potential with alternating sign along the different ydirection of the lattice. Using quantum Monte Carlo simulations and analytical calculations, the authors identify a bosonic weak topological insulator, characterized by a zero Chern number but nonzero Berry phase, which is manifested at either density 1/4 or 3/4, as determined by the potential pattern. They also map out the full phase diagram, including a chargedensitywave insulator at 1/2filling and superfluid at intermediate densities. Supprisely the weak topological insulator is further shown to be robust against any amount of nearestneighbor repulsion, as well as weak nextnearestneighbor repulsion. The proposed model may be experimentally realized using cold atoms in an optical lattice. I find the results are interesting from both theoretical and experimental aspects, so I recommend its publication.
I have the following comments:
1: a main character of weak topological insualtor is the existence of edge states on the edges along specific directions. Here the edge state is quasi1D superfluid. One may calculate the singleparticle correlator b^{dagger}_i b_j. The decaying behavior may reflect such information: it is insulating if the decay is exponential with the distance, and is gapless superfluid if the decay follows a power law.
2: Since the authors are studying a bosonic model, the Chern number and Berry phase for bosons should be calculated to characterize the bosonic weak topological insulator. as well as weak nextnearestneighbor repulsion. The experimental realization of our model is feasible in an optical lattice setup.
Report #1 by Anonymous (Referee 1) on 20201130 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2010.16126v2, delivered 20201130, doi: 10.21468/SciPost.Report.2245
Strengths
1  The paper is very well written and easy to follow.
2  The results are presented in an intuitive, pedagogical manner.
3  The authors perform a detailed study of their model, using multiple order parameters, topological invariants, as well as varying boundary conditions.
Weaknesses
1  The symmetry classification and topological protection of the model is insufficiently discussed (see report below).
2  Is it not clear to what extent the work meets the acceptance criteria of Scipost Physics (specifically, the list of "Expectations"), as opposed to Scipost Physics Core.1  The symmetry classification and topological protection of the model is insufficiently discussed (see report below).
2  Is it not clear to what extent the work meets the acceptance criteria of Scipost Physics (specifically, the list of "Expectations"), as opposed to Scipost Physics Core.
Report
The authors study the topological phases of hardcore bosons on a hexagonal lattice in which the onsite potential is modulated. They find that WTI phases appear once the onsite potential is larger than the nearest neighbor hopping strength, and that these phases are robust against NN repulsion as well as against weak NNN repulsion.
The paper is very well written. I enjoyed reading it. Results are presented in an intuitive, pedagogical way, making them easy to follow. There are however two points that I think the authors should address. These points are listed above, and I detail them here:
1) The authors discuss WTI phases appearing in symmetry class BDI and use a Hamiltonian that is noninteracting (I'm referring to Eq. 1, before the NN and NNN repulsion are added). However, the singleparticle Hamiltonian of Eq. 1 does not belong to symmetry class BDI. It does have timereversal symmetry T=K, meaning it is real, but there is no chiral symmetry. There is no unitary that anticommutes with H because of the nonzero onsite modulation and chemical potential.
Consistent with this lack of chiral symmetry, the edge states discussed by the authors do not appear at E=0. In class BDI, it is not just translation symmetry, but also chiral symmetry which protects the WTI. Because of chiral symmetry all states come in +E, E pairs (as can be seen from the bandstructures of Fig. 6). The edge states of a WTI should be pinned to the middle of the E=0 gap, such that they cannot be removed from this gap without breaking symmetries. In the authors' model however, edge states appear in the gap between bands 1 and 2 (or 3 and 4), away from E=0. What symmetry is responsible for their topological protection? Why can't they, in principle, be shifted up or down in energy such that they hybridize with the bulk states and dissapear?
2) While the work is novel and well presented, the authors should spend more time discussing if/how their paper meets the expectations of Scipost Physics (https://scipost.org/SciPostPhys/about#criteria). From my reading of the paper as it is now, it seems to me that it instead meets the acceptance criteria of Scipost Physics Core (https://scipost.org/SciPostPhysCore/about), provided that the point (1) above is addressed.
Requested changes
1  Show explicitly what are the symmetries of their model and its symmetry class.
2  Prove that their phases are topologically protected. This means to prove that there does not exist a symmetrypreserving perturbation which removes the edge states, for instance by shifting their energies away from their respective gaps.