## Implementing TEBD of open quantum chain in TenPy.

Discussing the best way to implement feature X
Sourav Nandy
Posts: 4
Joined: 03 Aug 2022, 11:30

### Implementing TEBD of open quantum chain in TenPy.

Dear,

I am interested to implement TEBD evolution of open system using the Lindblad Equations as discussed in , for example in https://core.ac.uk/download/pdf/196582653.pdf (Equation 2). In particular, I have in mind the following boundary driven scenario for Heisenberg chain.

$$d\tilde{\rho} = \mathcal{L} \tilde{\rho}$$,

where $$\tilde{\rho}$$ denotes the vectorised form of density matrix $$\rho$$. In vectorised form we have

$$\mathcal{L} = -i(H \otimes I - I\otimes H^{T})+\gamma/2(2\Gamma \otimes \Gamma^{*}-\Gamma^{\dagger}\Gamma \otimes I - I \otimes \Gamma^{T}\Gamma^{*})$$

where H is the Heisenberg Hamiltonian and the $$\Gamma$$ are quantum jump operators.

We have implemented such systems in ITensors and I am new to TenPy and not sure how to go about it in this package i.e., how to create the proper lattice, mps and mpo etc. However, I am very interested to implement it in TenPy for several reason. So, I would be grateful if you kindly let me know if there is some code for it in tenpy and if not then it would be nice if you could advice me on how can i implement such systems in TenPy.

Best,
Sourav
Johannes