Numerical implementation of creation and annhilation operators in the SSH model

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SUMMARY

This discussion focuses on the numerical implementation of creation and annihilation operators in the SSH model using density matrix formalism. The operators are defined as a_1 and a_1^\dagger, and the expressions a_1 ρ a_1^\dagger and a_1^\dagger ρ a_1 are central to the simulation. Participants provide insights on defining these operators for lattice models and their physical significance, particularly in relation to Lindblad dissipators. The conversation emphasizes the need for explicit matrix representations of these operators for effective numerical computation.

PREREQUISITES
  • Understanding of the SSH model in condensed matter physics
  • Familiarity with density matrix formalism
  • Knowledge of quantum mechanics operators, specifically creation and annihilation operators
  • Experience with numerical simulations in quantum systems
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  • Research the implementation of annihilation and creation operators in lattice models
  • Study the physical implications of Lindblad dissipators in quantum mechanics
  • Explore matrix representations of quantum operators for numerical simulations
  • Learn about density matrix evolution in open quantum systems
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Physicists, quantum computing researchers, and anyone involved in numerical simulations of quantum systems, particularly those working with the SSH model and density matrices.

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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