Graduate Numerical implementation of creation and annhilation operators in the SSH model

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The discussion focuses on implementing annihilation and creation operators in the SSH model using the density matrix formalism. The user seeks guidance on defining these operators for a lattice model and understanding the physical implications of expressions involving the density matrix, specifically a_1 ρ a_1† and a_1† ρ a_1. Additionally, they request tips or references for constructing these operators in matrix form for numerical simulations. The conversation emphasizes the need for clarity on both the mathematical construction and physical interpretation of these operators. Insights shared will aid in effectively simulating the SSH model.
JangMilad
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Hi all,

I'm working on a numerical simulation involving the SSH model and the density matrix formalism. I'm using annihilation and creation operators at the first site, denoted by a_1 and a_1^\dagger, and I'm trying to understand how to construct and compute expressions like:

a_1 \rho a_1^\dagger
a_1^\dagger \rho a_1

where \rho is the density matrix of the system.

My goal is to implement this numerically. I would appreciate any insights on:

How to define the annihilation/creation operators for a lattice model like SSH.

The physical meaning of the above expressions (e.g., in the context of Lindblad dissipators).

Any tips or references for constructing these operators explicitly in matrix form.

Thanks in advance for your help!
 
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