.. _sphx_glr_api_gallery_flat_bands:

Flat Bands
----------

The kagome and Lieb lattices' exactly flat bands, the natural home for
strong-correlation physics via Lieb's theorem.


.. raw:: html

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


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Some lattice geometries host a perfectly flat (dispersionless) band with uniform nearest-neighbor hopping alone -- destructive interference confines an eigenstate to a small loop of sites (a single hexagon on kagome, a single &quot;plus sign&quot; of four sites on Lieb) with exactly zero amplitude everywhere else, for every Bloch momentum simultaneously. A flat band&#x27;s macroscopic degeneracy is the natural home for strong-correlation physics: Lieb&#x27;s theorem guarantees the half-filled Hubbard model on a bipartite lattice with an unequal number of sites per sublattice (as Lieb&#x27;s own lattice has, 2 vs 1) is a ferromagnet, for any nonzero repulsion U -- one of the very few rigorous, non-perturbative results in the many-body problem. tbkit.lattices provides both lattices ready-made.">

.. only:: html

  .. image:: /api/gallery/flat_bands/images/thumb/sphx_glr_plot_flat_bands_thumb.png
    :alt:

  :doc:`/api/gallery/flat_bands/plot_flat_bands`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Flat-Band Lattices: Kagome and Lieb</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/flat_bands/plot_flat_bands