Numerical implementation of creation and annhilation operators in the SSH model

[JangMilad]

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!

 

[flippiefanus]

The ladder operators (annihilation and creation operators) do not individually represent physical processes. Therefore, it would not make sense to try and simulate them. Having said that, what one can do is to implement the mapping between the state before and after such an application of ladder operators. For a number state (Fock state), which is given by a Hermit-Gauss mode as a function of the position coordinate, it comes down the replacing one such mode with next one with one more or one less particle. If the state consists of a superposition of different Fock states, one need to use inner products to extract the coefficients and the construct the new state using these coefficients with the mapping of the Fock states. Hope that helps.