I have a problem when I used itensor to calculate the order phase of the Rydberg model with S=1/2 on the kagome lattice of this paper, as follows,
For this problem, this paper has a good explanation and provides a good solution.
To avoid spurious effects due to sharp edges, , we work with a geometry such that each unit cell at the right boundary of the cylinder contains only two sites. The resultant lattice, labeled as YC (2N2), has a noninteger number of unit cells, with a total ofN2Ă—(3N1+ 2) sites. Such a geometry has the added advantage of stabilizing the various ordered states.
we demonstrate that our results are qualitatively the same on lattices with and without an integer number of unit cells, and that a featureless liquid state exists in both cases. The specific density-wave profiles in the solid phases, however, may be sensitive to the jagged edges and can differ from those illustrated in the main text , as typified by the nematic order : this is because the boundaries seed two distinct symmetry-broken configurations from either end, which necessarily merge in the center of the system, forming a domain wall .
I’m trying to switch to a honeycomb lattice and find an order phase similar to above, but I’ve found that I seem to have a similar problem with jagged edges as above, and my similar calculations are as follows,
It can be seen that, calculate the <ni> when converged, there is a difference between excitation and value at the edge (the order of the last column is different from the previous columns, the value of green on edges is 0.9, in the middle of lattice is 0.7).
my question is:
Is there a way to avoid this problem in honeycomb latttice?
Whether it will affect my calculation of some specific parameters, such as the entanglement entropy of the order phase?
ls there any way to reduce or eliminate the impact?
Hi kevinh,
Looking at your results for the honeycomb lattice, I don’t immediately see anything that looks subtle, unexpected, or like a big problem. Is the problem you are seeing that the local properties are different at the edge from in the middle?
The problem described by the Semeghini paper is more about a density wave order that extends across the whole system, and it looks I guess something like the kagome plot at the top of your post where the density dips in the center of the system. But I don’t visually see any such dip in the center of your honeycomb plot - is there one?
Because I really don’t understand these issues deeply, the following are just some of my naive thoughts and curiosity.
In the original kagome lattice paper, considering , the order on the left and right sides of the lattice is different, the green in the first column is in the lower left corner of the unit cell, and the green in the last column is in the lower right corner of the unit cell. And this is similar to the situation in honeycomb, the order of the first column and the last column are not the same. I am trying to eliminate such differences.
Another problem is that it seems that the properties of the edges are different from those of the middle. For example, after enough scanning and convergence, the results of the middle columns and edge columns in honeycomb are not the same.Like this picture:
we can see that the left edge and right edge always seems to have its own fixed order that is different from each other, which necessarily merge in the center of the system, forming a domain wall.I think it might be due to the jagged edges.
These are some of my very naive questions. Thank you very much for your help and kindness. Maybe my idea is naive, but I am very willing to think about this problem.
Hi kevinh,
So the observations you are describing – things like the properties at the open edges being different from in the middle – are just how systems with open boundary conditions behave. There is basically no getting around this. The only real way to extract “bulk” physics – physics of the infinite system – from such open-boundary systems is to deduce properties in the center of the system which don’t depend anymore on the details of the edges. The main way to do this is to perform calculations on different size systems and extrapolate the results. There are sophisticated ways to do these extrapolations: for example, for simple local properties like the density the “subtraction method” is a really good way.
These issues and some ways to handle them are described in a fair bit of detail in the following review article: https://arxiv.org/abs/1105.1374
So overall I would say the things you are seeing aren’t really “problems” as much as just what open-boundary systems are like. Note that as described in the article above, some of these “problems” can actually be opportunities, such as the opportunity to apply “pinning fields” to the open edges to pin various orders in the bulk, which can make these orders stronger and more apparent and lead to more robust extrapolations.
