Ground state fidelity of Luttinger liquids: a wavefunctional approach

Abstract

We use a wavefunctional approach to calculate the fidelity of ground states inthe Luttinger liquid universality class of one-dimensional gapless quantummany-body systems. The ground state wavefunctionals are discussed using boththe Schrödinger (functional differential equation) formulation and a path integralformulation. The fidelity between Luttinger liquids with Luttinger parametersK and K′ is found to decay exponentially with system size, and to obey the symmetryF(K,K′) = F(1/K,1/K′) as a consequence of a duality in the bosonization description of Luttinger liquids.