About long-range interaction

How do I use this algorithm? What does that parameter do?
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Posts: 13
Joined: 11 Mar 2020, 01:07

About long-range interaction

Post by steven_tao »

Dear TeNPy community:

1. I am simulating the 1D long-range Ising chain with power-law interaction, could anyone tell me how set the long-range Ising Hamiltonian in TeNPy? If I want to calculate the half-chain entanglement using iDMRG, how I should cut the chain and how I choose the length of the chain? For the Ising chain with only nearest-neighbor interaction, we can set the chain length of two, then calculate the entanglement using iDMRG. But how to set it for the long-range chain? In addition, the TDVP can be used for the long-range case?

\(H_{IS} = \sum_{j>i}^L \frac{1}{(j-i)^\lambda} \sigma_i^z \sigma_j^z + h \sum_i \sigma_i^x\)

2. If this 1D long-range Ising chain is coupled to e.g., 1D XX model at the end chain of 1D Ising model, how we can we set the model in TeNPy ?

\(H_{XX} = J \sum_{i-j=1, j=L+1}^{2L} \tau_i^x \tau_j^x \),

\(H_{coupled} = J \sigma_L^x \tau_{L+1}^x \).

Thank you very much.
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