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

TL;DR

This paper develops a wave functional method to compute the ground-state fidelity in Luttinger liquids, revealing exponential decay with system size and a duality symmetry in the fidelity measure.

Contribution

It introduces a wave functional approach to analyze ground-state fidelity in Luttinger liquids, highlighting duality symmetry and exponential decay behavior.

Findings

Fidelity decays exponentially with system size.

Fidelity obeys a duality symmetry F(K,K')=F(1/K,1/K').

Wave functional approach provides new insights into Luttinger liquids.

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.