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

Abstract

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 Schrodinger (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.

13 pages, IOP single-column format. Sec. 3 expanded with discussion of short-distance cut-off. Some typos corrected. Ref. 44 in v2 is now footnote 2 (moved by copy editor). Published version

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• Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement
• Escort distribution function of work done and diagonal entropies in quenched Luttinger liquids
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model