XXZChain antiferromagnet showing no entanglement?

How do I use this algorithm? What does that parameter do?
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XXZChain antiferromagnet showing no entanglement?

Post by Adipta »

Hi, I just started using TeNPy. I was trying to simulate the XXZChain in Google Colab with parameters, Jxx = 1. , Jz = 2., hz = 0 with tebd.Engine but it keeps giving back zero in the entanglement_spectrum. Here is my code:

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tebd_params = {'order': 2, 'delta_tau_list': [0.1, 0.001, 1.e-5],
               'max_error_E': 1.e-6, 
               'trunc_params': {'chi_max': 50, 'svd_min': 1.e-10}}

M = XXZChain({'L': 100, 'Jxx': 1., 'Jz': 2., 'hz': 0., 'bc_MPS': 'finite'})

product_state = ['up'] * M.lat.N_sites
psi = MPS.from_product_state(M.lat.mps_sites(), product_state, bc = M.lat.bc_MPS)
eng = tebd.Engine(psi, M, tebd_params)

What am I doing wrong here? Thanks in advance :) .

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Re: XXZChain antiferromagnet showing no entanglement?

Post by Johannes »

The all-up state is an exact eigenstate of the model and hence won't evolve in time, in particular if you use Sz-conservation (which you do in this case): the all-up state is the only state in the sector with \(S_{total} = L/2\).
Try starting from a different state, e.g. all up but one spin down (which is still a very trivial problem, or with an initial state of Neel form

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product_state = ['up', 'down'] * (M.lat.N_sites //2)  # assuming that M.lat.N_sites is odd

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