Quantum phase transition, quantum fidelity and fidelity susceptibility in the Yang–Baxter system

Abstract

In this paper, we investigate the ground-state fidelity and fidelity susceptibility in the many-body Yang---Baxter system and analyze their connections with quantum phase transition. The Yang---Baxter system was perturbed by a twist of $$ e^{i\varphi } $$ei? at each bond, where the parameter $$ \varphi $$? originates from the q-deformation of the braiding operator U with $$q = e^{-i\varphi }$$q=e-i? (Jimbo in Yang---Baxter equations in integrable systems, World Scientific, Singapore, 1990), and $$ \varphi $$? has a physical significance of magnetic flux (Badurek et al. in Phys. Rev. D 14:1177, 1976). We test the ground-state fidelity related by a small parameter variation $$\varphi $$? which is a different term from the one used for driving the system toward a quantum phase transition. It shows that ground-state fidelity develops a sharp drop at the transition. The drop gets sharper as system size N increases. It has been verified that a sufficiently small value of $$\varphi $$? used has no effect on the location of the critical point, but affects the value of $$ F(g_{c},\varphi ) $$F(gc,?). The smaller the twist $$\varphi $$?, the more the value of $$ F(g_{c},\varphi ) $$F(gc,?) is close to 0. In order to avoid the effect of the finite value of $$ \varphi $$?, we also calculate the fidelity susceptibility. Our results demonstrate that in the Yang---Baxter system, the quantum phase transition can be well characterized by the ground-state fidelity and fidelity susceptibility in a special way.