Ground state fidelity of Luttinger liquids: a wavefunctional approach

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