A physical understanding of fractionalization

Question

all! Is there a physical understanding of fractionalization in condensed matter physics? The textbook approach is theoretical, not physical. I'm thinking of spin-charge separation for electrons, the fractional quantum hall effect, and things like that. The theoretical approach is to introduce an auxiliary gauge field with no kinetic term at the bare level so that it is apparently confining and nondynamical at the bare level, but somehow, dynamics intervenes, and it becomes deconfining, and somehow, there's some mixture between the emergent gauge symmetry and the original symmetries, and somehow, fractionalization comes in in the diagonalization.

What is the physical interpretation without introducing theoretical auxiliary gauge symmetries right from the onset?

Answer 1

Beyond one dimension, fractionalization is always associated with emergent gauge theory. Emergent gauge theory can (some times) be understood from string-net condensation. In this case, quasiparticles with fractional quantum numbers are always defects that correspond to "ends of strings" (see a discussion here). One way to understand why ends of strings can carry fractional quantum number is to note that we can never create a single end of string alone. Ends of string always appear in pairs and the pair has no fractional quantum number, but each end can and does carry fractional quantum number.

Another way to get fractionalization is through FQH effect. So far, we do not have a unified theory that cover both cases. However, I believe that the long range entanglements (ie topological order) is the physical origin of fractionalization. See also Topological Charge. What is it Physically?