I have solved the 2D Sandvik model (J-Q model) using DMRG and found the ground state which is an MPS. But I need to verify if this MPS is a VBS(valence bond solid) how do I do that?
Do you know of a measurement you could make of the state that would identify it as a VBS, like an order parameter, entanglement properties, etc.?
There is something called as dimer dimer correlation but I am not sure if my results are correct for that. So I wanted to know if there is any measure or any way to find if the mps is a vbs or antiferromagnetic
You can measure the dimer-dimer correlator of an MPS, that should be straightforward.
Can you help me with that I am unable to write the formula into my code properly. I have attached the formula for the same.
Hi Vaibhav,
The first type of correlator you write there C_s is a “two-point” correlator, which is a linear combination of correlators of a form like
C_s(r) = \langle S^z_0 S^z_r \rangle + \frac{1}{2} \langle S^+_0 S^-_r \rangle + \frac{1}{2} \langle S^-_0 S^+_r \rangle
So you can compute each of those three terms separately then add them together. A convenient way to compute each term is to use the correlation_matrix function included in the ITensorMPS package. For documentation on that you can look at this link:
https://docs.itensor.org/ITensorMPS/stable/MPSandMPO.html#ITensorMPS.correlation_matrix-Tuple{MPS,%20AbstractString,%20AbstractString}
For the other C_d correlator which is a four-point correlator, you may want to try the ITensorCorrelators package at this link:
https://github.com/ITensor/ITensorCorrelators.jl
and follow a similar strategy as what I mentioned above of breaking the correlation functions down into sums of products of operators.