Hi,

First, this is a general question about ITensor or DMRG.

So, I am recently playing with the SU(2)-symmetric spin-1 Bilinear-Biquadratic Heisenberg model using Itensor.

$$

H=\cos\theta\sum_{i, j} S_i\cdot S_j+\sin\sum_{i,j} (S_i\cdot S_j)^2

$$

The Hamiltonian itself is SU(2)-symmetric. When tuning the paramters, however, there will be some phases where the ground states spontaneously break the SU(2) spin-rotational symmetry. Since for now ITensor does not have SU(2) symmetric version (I am not sure whether you will consider about this in the future), I think it will be difficult to capture the spontaneous symmetry breaking.

But if one insists on doing this, I am wondering how one should proceed. Here I will share some ideas that I know from different literatures. And say, now we want to capture the Neel (AFM) order.

(1) Calculate the staggered magnetization.

$$

|\vec{M}| = |\sum_{i}(-1)^i \vec{S}_i|

$$

This might not be a good idea for models whose ground states spontaneously break the SU(2) symmetry because we are dealing with finite systems. If I remember it correctly, there is no spontaneous symmetry breaking (symmetry of the Hamltonian) for (d<2) finite systems.

(2) Correlations.

The spin-spin correlations for Neel-order states will have a non-vanishing oscillating tail. And it is SU(2) symmetric and thus respects the symmetry of the Hamtilonian.

And one can have some neel order parameter, e.g., see this paper.

$$

m_s^2=\frac{1}{N^2}\sum_{ij}(-1)^{r_i - r_j} S_i\cdot S_j

$$

(3) Manually breaking the symmetry by pinning fields.

$$

H = H_0 + h\sum_i (-1)^i S_z

$$

And eventually we make h go to zero. This seems to take a little bit more effort on calculations.

This question is a bit specific, but I think it is worth discussions because it will be helpful and give some ideas for those who want to study similar Heisenberg spin models using Itensor. And I would very much appreciate it if you have any advice on this.

Thank you very much!

Best,

Yi