.. _sphx_glr_api_gallery_condensed_anderson_localization:

Anderson Localization
---------------------

The 1958 discovery that disorder alone, with no interactions, can halt
diffusion: exponentially localized eigenstates on a disordered 1D chain,
diagnosed by the inverse participation ratio and localization length.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Philip Anderson showed that random onsite disorder, at any nonzero strength, exponentially localizes every eigenstate of a 1D tight-binding chain (~physicskit.condensed.anderson_localization.anderson_chain_hamiltonian). The inverse participation ratio (~physicskit.condensed.anderson_localization.inverse_participation_ratio) distinguishes extended states (\text{IPR}\sim 1/N) from localized ones (\text{IPR}=O(1)), and localization_length extracts the decay length \xi directly from an eigenstate&#x27;s envelope.">

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  .. image:: /api/gallery/condensed/anderson_localization/images/thumb/sphx_glr_plot_anderson_localization_thumb.png
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  :doc:`/api/gallery/condensed/anderson_localization/plot_anderson_localization`

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      <div class="sphx-glr-thumbnail-title">Anderson Localization: Disorder Halts Diffusion</div>
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    </div>


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   /api/gallery/condensed/anderson_localization/plot_anderson_localization