Construct lattice operators isolating subleading continuum operators

Construct lattice operators whose dominant continuum contributions are subleading operators in both the \(\mathbb{Z}_2\)-even and \(\mathbb{Z}_2\)-odd sectors of the one-dimensional long-range Ising conformal field theory.

Background

The paper identifies the controlled construction of lattice observables dominated by subleading continuum operators as an unresolved target for Monte Carlo studies of the one-dimensional long-range Ising conformal field theory. Such operators would enable direct measurements of subleading conformal data, including the shadow-pair operator ϕ3\phi^3 in the odd sector and the operator ϕ4\phi^4 in the even sector. The challenge is to suppress overlap with leading operators while retaining adequate statistical precision and control over finite-distance and smearing effects.

References

There are many interesting open targets to further expand the breadth of the 1d LRI as a playground for CFT. First, a controlled construction of lattice operators whose dominant continuum contribution are subleading operators, both in the \mathbb{Z}_2 even and \mathbb{Z}_2 odd sectors opens the door for the measurement of many interesting observables.

— Field theory guides Monte Carlo in the one-dimensional long-range Ising model  (2610.26838 - Antunes et al., 19 Oct 2026) in Section Discussion