nLab Heisenberg model



Solid state physics

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In solid state physics

In solid state physics, the Heisenberg model is spin chain-model for magnetic quantum materials.

The Heisenberg model is akin to the Ising model, but where the latter only has internal symmetry-group / 2 \mathbb{Z}/2 (spin flips along one axis), the Heisenberg model has the full Spin(3) \simeq SU(2)-group of internal symmetries acting on spin representations located at each of the “sites” of the model.

There are generalizations of the model with SU ( N ) SU(N) -internal symmetry for any NN \in \mathbb{N}.

In SYM theory and AdS/CFT

As an abstract model, the Heisenberg spin chain has a curious re-incarnation as describing the dynamics of BMN operators in D=4 N=4 super Yang-Mills theory under the dilatation operator in the large-N limit of the AdS/CFT correspondence. See here for more.


Symmetry protected topological phase

The Heisenberg model has a curious internal-symmetry protected topological phase, observed in Haldane 1983 and hence known as the Haldane phase.



See also:


On symmetry protected topological phases of the Heisenberg model:

Created on May 16, 2022 at 17:00:24. See the history of this page for a list of all contributions to it.