1.

*Adiabatic continuity.*

As one gradually turns on the interactions the excited states of the system smoothly evolve from those in the non-interacting system. As a result the quasi-particles have the same quantum numbers and statistics as the constituent particles. The most prominent example is in Landau's Fermi liquid theory which describes elemental metals and liquid 3He.

2.

*Adiabatic discontinuity.*

The quasi-particles do NOT have the same quantum numbers and statistics as the constituent particles. One example, is magnons (spin waves) in a spin-1/2 Heisenberg antiferromagnet. They have spin one and act like bosons. In contrast, the constituent particles are localised electron that are fermions with spin-1/2. An even more dramatic example occurs in the fractional quantum Hall effect. The constituent particles are electrons with charge -e and obey Fermi-Dirac statistics. But, the quasi-particles have fractional charge and obey anyon statistics.

This was recently stressed by Brijesh Kumar after a talk I gave.

The distinction is interesting because if you use Berry's criteria for emergence [a singular asymptotic expansion] (which I do like) then only in the second case would you define the quasi-particles as emergent.

The figure above describing adiabatic continuity is from Piers Coleman.

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