Implementing TEBD of open quantum chain in TenPy.

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Sourav Nandy
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Joined: 03 Aug 2022, 11:30

Implementing TEBD of open quantum chain in TenPy.

Post by Sourav Nandy »


I am interested to implement TEBD evolution of open system using the Lindblad Equations as discussed in , for example in (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.

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Re: Implementing TEBD of open quantum chain in TenPy.

Post by Johannes »

Hi Sourav,
cool, great to hear that you want to implement this in TeNPy! There's different ways to implement Lindblad evolution, so before we discuss TeNPy, we should maybe discuss a bit which way you want to implement it, and it's probably much easier to do this over zoom. I'll contact you by email to arrange a meeting.
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