- #1
Dhiman9163
- 1
- 0
- TL;DR
- I am trying to solve the system using exact diagonalization
I want to simulate a spin polarized SSH model with Hamiltonian of the form
$$\hat{H} = v \sum_{i = 1}^N (\hat{C}_{i,A}^\dagger \hat{C}_{i,B} + h.c.) + w \sum_{i = 1}^N (\hat{C}_{i+1,A}^\dagger \hat{C}_{i,B} + h.c.) + V_1 \sum_{i = 1}^N \hat{n}_{i, A}\hat{n}_{i, B} + V_2 \sum_{i = 1}^N \hat{n}_{i+1, A}\hat{n}_{i, B}$$
I have already simulated the non-interacting part, which works fine. The code for it can be seen [here][1]. But when I include the interacting part, the Hamiltonian matrix become non-hermitian. The code for the interacting system can be seen [here][2].\
From the analytical Hamiltonian, it is clear that the Hamiltonian matrix should be Hermitian. Therefore, I have made some mistake while implementing it. But I can not understand what the mistake is or how to fix it. Can anyone help me do that?
[1]: https://github.com/dhimankchakraborty/Non-Interacting-SSH-Model-without-Spin
[2]: https://github.com/dhimankchakraborty/Interacting-SSH-Model-without-Spin/blob/main/test_01.ipynb
$$\hat{H} = v \sum_{i = 1}^N (\hat{C}_{i,A}^\dagger \hat{C}_{i,B} + h.c.) + w \sum_{i = 1}^N (\hat{C}_{i+1,A}^\dagger \hat{C}_{i,B} + h.c.) + V_1 \sum_{i = 1}^N \hat{n}_{i, A}\hat{n}_{i, B} + V_2 \sum_{i = 1}^N \hat{n}_{i+1, A}\hat{n}_{i, B}$$
I have already simulated the non-interacting part, which works fine. The code for it can be seen [here][1]. But when I include the interacting part, the Hamiltonian matrix become non-hermitian. The code for the interacting system can be seen [here][2].\
From the analytical Hamiltonian, it is clear that the Hamiltonian matrix should be Hermitian. Therefore, I have made some mistake while implementing it. But I can not understand what the mistake is or how to fix it. Can anyone help me do that?
[1]: https://github.com/dhimankchakraborty/Non-Interacting-SSH-Model-without-Spin
[2]: https://github.com/dhimankchakraborty/Interacting-SSH-Model-without-Spin/blob/main/test_01.ipynb