Ground-state fidelity of Luttinger liquids: A wave functional approach

We use a wave functional 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 wave functionals 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. Keywords: bosonization, Luttinger liquids (theory), quantum phase transitions (theory).Ground-state fidelity of Luttinger liquids: A wave functional approach 2 1.