Relate lattice Bell-pair crosscap states to conformal crosscap states

Establish the precise correspondence between lattice crosscap states constructed by maximally entangling antipodal sites (Bell pairs) in integrable spin chains and conformal crosscap states in 1+1-dimensional conformal field theories, including how these lattice constructions map to continuum crosscap boundary conditions and coefficients.

Background

Recent works in integrable models have implemented lattice crosscap states by pairing antipodal sites into Bell states and analyzed overlaps with eigenstates via determinant formulas. However, the continuum CFT significance of these lattice constructions remains unclear.

A rigorous mapping between lattice Bell-pair crosscaps and conformal crosscap states would unify lattice and field-theoretic perspectives, enabling the extraction of universal CFT data (such as Luttinger parameters) directly from lattice wave functions and clarifying the physical interpretation of integrable boundary state overlaps.