We study the ground state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground state transitions under different tilt values. For a very small tilt (for example $10^{-10}$), two transitio
ns are found. For a moderate tilt (for example $10^{-3}$), only one transition is found. For a large tilt (for example $10^{-1}$), no transition is found. We explain this by analyzing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with particle number $N$. This means for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large-$N$ limit it can be.
We study the zero temperature quantum dynamical critical behavior of the anisotropic XY chain under a sudden quench in a transverse field. We demonstrate theoretically that both quench magnetic susceptibility and two-particle quench correlation can b
e used to describe the dynamical quantum phase transition (QPT) properties. Either the quench magnetic susceptibility or the derivative of correlation functions as a function of initial magnetic field $a$ exhibits a divergence at the critical points when final magnetic field $b$ is fixed. A special case that final magnetic field $b$ is just at the critical point is discussed separately. Some of the critical exponents of the dynamical QPT are obtained and the long-range correlation of the quench system is analyzed. We also compare our result with that of the static QPT.
We investigate the 2D weakly interacting Bose-Einstein condensate in a rotating trap by the tools of quantum information theory. The critical exponents of the ground state fidelity susceptibility and the correlation length of the system are obtained
for the quantum phase transition when the frst vortex is formed. We also find the single-particle entanglement can be an indicator of the angular momentums for some real ground states. The single-particle entanglement of fractional quantum Hall states such as Laughlin state and Pfaffian state is also studied.
