Strongly-correlated systems are interesting yet hard to solve. However, even in the absence of the weak-coupling parameter, a theory might have a nice sector where it might become solvable. We found that the sector of large-charge is an instance of this — The coupling constant effectively gets suppressed by the inverse charge, when the theory has a global symmetry. In this talk, I will explain the method of the large-charge expansion, taking an example of the complex phi^4 theory in three dimensions, which describes the phase transition of superfluid Helium-4. We will see that the scaling dimension of the operator phi^J goes as O(J^{3/2}), contrary to the weak-coupling expectation, O(J). I will also compare the analytic result with lattice data, showing that the large-charge expansion works surprisingly well even at small-charge.

https://indico.math.cnrs.fr/event/9428/