Quantum Field theory vs. many-body Quantum Mechanics

[Fractal matter]

Some effects may be described by topological effective field theory, in which case it may not have quasiparticle excitations.

Can you give an example please ? I'm interested in all the cases in which the effective theory doesn't have quasiparticles.

 

[Demystifier]

Can you give an example please ? I'm interested in all the cases in which the effective theory doesn't have quasiparticles.

All topological field theories lack propagating degrees of freedom and hence (quasi)particles. An example of topological field theory is Chern-Simons theory. In condensed matter, it plays a role in a description of quantum Hall effect (see e.g. https://arxiv.org/abs/1606.06687). Roughly speaking, in the quantum Hall effect the EM field interacts with matter in such a way that the effective dressed EM field cannot propagate through the material, so the dressed EM field does not have dressed photon excitations.