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Certain quantum phase transitions are characterized by the emergence of some ordering wavevector $K$ : antiferromagnetism, charge or spin density waves, among others.

In the case of Néel antiferromagnetism, the wavevector $K = (\pi, \pi)$ breaks the Fermi surface into several pockets, as can be seen on the picture below. This phenomenon is usually referred to as "Fermi surface reconstruction" : see for instance this, or this: qpt.physics.harvard.edu/talks/sces11.pdf paper.

enter image description here

I don't understand how the quantum ordering is able to change the Fermi surface as such. What is the effect on the low-lying excitations ?

Also, some of these pockets are called "electron pockets", while the other are referred to as "hole pockets". I am a bit puzzled on how to distinguish one from the other, and what is the meaning of this terminology.

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    $\begingroup$ The interior of an electron pocket is filled with electrons. The interior of a hole pocket is empty. $\endgroup$ – leongz May 2 '16 at 22:00

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