Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions.

The fidelity is widely used to detect quantum phase transitions, which is characterized by either a sharp change of fidelity or the divergence of fidelity susceptibility in the thermodynamical limit when the phase-driving parameter is across the transition point. In this work, we unveil that the occurrence of exact zeros of fidelity in finite-size systems can be applied to detect quantum phase transitions. In general, the fidelity F(γ,γ[over ̃]) always approaches zero in the thermodynamical limit, due to the Anderson orthogonality catastrophe, no matter whether the parameters of two ground states (γ and γ[over ̃]) are in the same phase or different phases, and this makes it difficult to distinguish whether an exact zero of fidelity exists by finite-size analysis. To overcome the influence of orthogonality catastrophe, we study finite-size systems with twist boundary conditions, which can be introduced by applying a magnetic flux, and demonstrate that exact zeros of fidelity can be always accessed by tuning the magnetic flux when γ and γ[over ̃] belong to different phases. On the other hand, no exact zero of fidelity can be observed if γ and γ[over ̃] are in the same phase. We demonstrate the applicability of our theoretical scheme by studying concrete examples, including the Su-Schrieffer-Heeger model, Creutz model, and Haldane model. Our work provides a practicable way to detect quantum phase transitions via the calculation of fidelity of finite-size systems.

Stimuli-responsive grating with a tunable period and a diffraction order.

The next-generation diffraction grating not only requires a nonmechanical control and a remote control to generate a diffraction pattern but also requires a tunable period. Here, we propose a stimuli-responsive liquid crystal (LC) phase grating with a tunable period and a diffraction order. The stimuli-responsive LC diffraction grating is composed of periodically arranged electrodes on a double-sided glass substrate. By adjusting the driving scheme, the pitch and diffraction order of the LC grating can be switched between three different modes. The experimental results show that the LC grating has a lower driving voltage (∼5 V). In addition, the tunable LC grating can achieve more diffraction orders, which can be applied to a holographic display to achieve a wide-viewing angle and an enlarged size.