We revisit the anyon gas in a solvable large-charge limit, where the particle number N and the statistical coupling parameter k are taken to infinity with N/k held fixed. In this near-bosonic regime, the statistical interaction 1/k is weak, while its collective effects remain finite. We find a crystalline ground state with O(N/k) lattice sites, in which the long-range statistical interactions are completely screened, yielding a conventional crystal without superfluidity. Our results suggest a quantum phase transition from a crystal at k > k_c to a superfluid at k < k_c, with k_c ≃ 2–5, challenging the expectation that statistical interactions alone necessarily produce superfluidity. We also discuss how the large-charge expansion captures qualitative and quantitative features beyond its regime of strict validity.

We revisit the anyon gas in a solvable large-charge limit, where the particle number N and the statistical coupling parameter k are taken to infinity with N/k held fixed. In this near-bosonic regime, the statistical interaction 1/k is weak, while its collective effects remain finite. We find a crystalline ground state with O(N/k) lattice sites, in which the long-range statistical interactions are completely screened, yielding a conventional crystal without superfluidity. Our results suggest a quantum phase transition from a crystal at k > k_c to a superfluid at k < k_c, with k_c ≃ 2–5, challenging the expectation that statistical interactions alone necessarily produce superfluidity. We also discuss how the large-charge expansion captures qualitative and quantitative features beyond its regime of strict validity.

The large charge approach allows to describe special sectors of strongly-coupled systems. When another controlling parameter is present, it is still useful because it allows to unveil interesting mathematical structures and access previously unexplored parts of the spectrum. In this talk I will concentrate on the bosonic O(N) vector model and the fermionic NJL model in the large-N limit, give a geometrical interpretation of the asymptotic expansion of the dimension of the lowest operator of fixed charge, and use resurgence to resum this expansion. The results suggest a novel and still unexplored interplay between conformal symmetry and resurgence, offering an intuitive interpretation for the striking agreement of the large-charge predictions with lattice data, even in the case of the O(2) model.

We study the unitary Fermi gas in an external trap in the double-scaling limit of large flavor number N and large charge Q at fixed Q/N. At leading order, the problem reduces to the spectral zeta function of a BdG operator in an inhomogeneous pairing background. The grand potential admits a gradient expansion with distinct bulk and edge sectors. We show that when the trap is harmonic, the bulk sector expansion terminates: beyond the first three terms every bulk contribution integrates to zero. This cancellation is general and follows from zeros of the Euler beta function computed in the Son-Wingate effective field theory, independent of the low-energy constants. The truncation persists for anisotropic traps in any odd dimension. All higher-order dependence for harmonic potentials is therefore carried by the droplet edge. For anharmonic traps, the asymptotic bulk series is factorially divergent. Using a heat-kernel WKB analysis, we show that its large-order growth, sign oscillations, and optimal truncation are fixed by complex periodic orbits of the BdG problem, which are analytic continuations of Andreev reflections. We numerically confirm the predicted Borel singularities for quartic and sextic traps.

We revisit the long-standing problem of the anyon gas. We study the solvable near-bosonic limit of a large number of anyons N at fixed N/k, where 1/k characterizes the statistical interaction. In this limit, the ground state is a crystal with order N/k lattice sites. The statistical interactions, mediated by a long-range gauge field, are completely screened within the crystalline phase. The resulting state is a conventional crystal without superfluidity. We characterize this anyon crystal by determining its unit-cell size, ground-state energy, acoustic excitations, angular momentum crossings, and other properties. Our results indicate a quantum phase transition between the crystal at k>kc​ and a superfluid at k<kc​, with a critical value kc​≃2–5. These results imply that an anyon gas with only statistical interactions is not necessarily a superfluid, contrary to common lore. We also present a detailed analysis of the renormalization-group evolution of anyon–anyon interactions, identifying many new potential fixed points and elucidating finite-size effects.

We investigate the odd-even staggering in the harmonically-trapped unitary Fermi gas at large particle-number charge Q. Using both a large-NN BdG description and a complementary large-charge EFT method, we show that for odd particle number the extra fermion forms an edge-localized quasiparticle near the Thomas-Fermi surface rather than a bulk excitation. In the edge limit, the microscopic BdG problem reduces to a universal coupled Airy system whose lowest positive eigenvalue fixes the leading odd-even splitting energy, $\chi \xi^{1/6} (24 Q)^{1/9}$, where $ξ$ is the Bertsch parameter, and $\chi$ is a universal edge coefficient. The associated EFT describes a fermionic mode confined to the boundary and coupled to the superfluid Goldstone field, reproducing the same QQ scaling while introducing a dependence on two low-energy constants. Finally, we numerically compute the spectrum and confirm the predicted scaling and localization properties.