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arXiv · 1804.06495

Observables in Inhomogeneous Ground States at Large Global Charge

Simeon Hellerman·Nozomu Kobayashi·Shunsuke Maeda·Masataka Watanabe
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Abstract

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 $\rho_1/\rho_2\ll 1$. 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.

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Simeon Hellerman, Nozomu Kobayashi, Shunsuke Maeda, Masataka Watanabe. 2018-04-17. Observables in Inhomogeneous Ground States at Large Global Charge. https://doi.org/10.1007/jhep08(2021)079

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