Observables in inhomogeneous ground states at large global charge

As a sequel to previous work, we extend the study of the ground state configuration of the D = 3, Wilson-Fisher conformal O(4) model. In this work, we prove that for generic ratios of two charge densities, rho(1)/rho(2), the ground-state configuration is inhomogeneous and that the inhomogeneity expresses itself towards longer spatial periods. This is the direct extension of the similar statements we previously made for rho(1)/rho(2) << 1. We also compute, at fixed set of charges, rho(1), rho(2), the ground state energy and the two-point function(s) associated with this inhomogeneous configuration on the torus. The ground state energy was found to scale (rho(1) + rho(2))(3/2), as dictated by dimensional analysis and similarly to the case of the O(2) model. Unlike the case of the O(2) model, the ground also strongly violates cluster decomposition in the large-volume, fixed-density limit, with a two-point function that is negative definite at antipodal points of the torus at leading order at large charge.

Automated summary

In this study, we extend previous work on the ground state configuration of the D = 3, Wilson-Fisher conformal O(4) model, showing that for generic ratios of charge densities, the ground-state configuration is inhomogeneous. The ground state energy scales with (rho(1) + rho(2))(3/2) and violates cluster decomposition in the large-volume, fixed-density limit, with a negative definite two-point function at antipodal points of the torus at large charge.