We calculate the fidelity susceptibility ${\chi }_f$ for the Luttinger model and show that there is a universal contribution linear in temperature $T$ (or inverse length $1/L$). Furthermore, we develop an algorithm—based on a lattice path integral approach—to calculate the fidelity $F(T)$ in the thermodynamic limit for one-dimensional quantum systems. We check the Luttinger model predictions by calculating ${\chi }_f(T)$ analytically for free spinless fermions and numerically for the $XXZ$ chain. Finally, we study ${\chi }_f$ at the two phase transitions in this model.

• Received 13 June 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.117203