Fidelity and entanglement entropy for infinite-order phase transitions

Abstract

Here, we study the fidelity and the entanglement entropy for the ground states of quantum systems that have infinite-order quantum phase transitions. In particular, we consider the quantum O(2) model with a spin-S truncation, where there is an infinite-order Gaussian (IOG) transition for S = 1 and there are Berezinskii-Kosterlitz-Thouless (BKT) transitions for S ≥ 2. We show that the height of the peak in the fidelity susceptibility (χ F ) converges to a finite thermodynamic value as a power law of 1 / L for the IOG transition and as 1 / ln (L) for BKT transitions. The peak position of χ F resides inside the gapped phase for both the IOG transition and BKT transitions. On the other hand, the derivative of the block entanglement entropy with respect to the coupling constant $S^{'}_{vN}$ has a peak height that diverges as ln 2 (L) for S = 1 and ln 3 (L) for S ≥ 2 and can be used to locate both kinds of transitions accurately. We include higher-order corrections for finite-size scalings and obtain the value of the central charge consistent with c = 1 predicted by conformal field theory. The crossing point of χ F between different system sizes is at the IOG point for S = 1 but is inside the gapped phase for S ≥ 2, while those of $S^{'}_{vN}$ are at the phase-transition points for all S truncations. Our work elaborates on how to use the finite-size scaling of χ F or $S^{'}_{vN}$ to detect infinite-order quantum phase transitions and discusses the efficiency and accuracy of the two methods.