Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric $\phi^4$ theory with $n\to -2$ and loop-erased random walks

Understand

Driven periodic elastic systems such as charge-density waves (CDWs) pinned by impurities show a non-trivial, glassy dynamical critical behavior.

• Their proper theoretical description requires the functional renormalization group.
• We show that their critical behavior close to the depinning transition is related to a much simpler model, $O(n)$-symmetric $\phi^4$ theory in the unusual limit of $n\to -2$.
• We demonstrate that both theories yield identical results to 4-loop order and give both a perturbative and a non-perturbative proof of their equivalence.