Mixed Scalar-Current bootstrap in three dimensions

TL;DR

This paper employs numerical bootstrap methods to analyze mixed scalar-current correlation functions in three dimensions, providing new bounds on operator coefficients and thermal properties in the $O(2)$ model, with implications for condensed matter physics.

Contribution

It introduces a mixed scalar-current bootstrap approach in 3D, deriving bounds on three-point functions and thermal observables in the $O(2)$ model, extending the scope of conformal bootstrap techniques.

Findings

Bounds on three-point function coefficients involving currents and scalars.

Estimates of thermal one-point functions from bootstrap and Monte Carlo data.

New constraints on operator dimensions and sectors in the $O(2)$ model.

Abstract

We study the mixed system of correlation functions involving a scalar field charged under a global $U(1)$ symmetry and the associated conserved spin-1 current $J_\mu$. Using numerical bootstrap techniques we obtain bounds on new observables not accessible in the usual scalar bootstrap. We then specialize to the $O(2)$ model and extract rigorous bounds on the three-point function coefficient of two currents and the unique relevant scalar singlet, as well as those of two currents and the stress tensor. Using these results, and comparing with a quantum Monte Carlo simulation of the $O(2)$ model conductivity, we give estimates of the thermal one-point function of the relevant singlet and the stress tensor. We also obtain new bounds on operators in various sectors.