Monday, March 22, 2010

Geometric frustration of kinetic energy

Just as one can discuss geometrical frustration of spins in antiferromagnets one can also discuss geometrical frustration of the kinetic energy of electrons on similar lattices.
But it should also be noted that this is a strictly quantum mechanical effect arising from quantum interference. This is in distinct contrast to geometrical frustration in antiferromagnets which can occur for purely classical spins.

A few years ago, Jaime Merino, Ben Powell, and I discussed trying to quantify this kinetic energy frustration. (See Section IIC of this long PRB paper). In a non-interacting electron model the only proposal we were aware of for a quantitative measure of this frustration of the kinetic energy was due to Barford and Kim:

I am wondering if the width of the lowest lying band of triplet excitations may be a good measure of frustrations in a quantum antiferromagnet. More on that later...

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