Finite-Temperature Fidelity Susceptibility for One-Dimensional Quantum Systems

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 $1/L$) by using conformal field theory. 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.\\*[0.2cm] J. Sirker, PRL {\bf 105}, 117203 (2010)