Scaling dimension of fidelity susceptibility in quantum phase transitions

Abstract

We analyze ground-state behaviors of fidelity susceptibility (FS) and show that the FS has its own distinct dimension instead of real system's dimension in general quantum phases. The scaling relation of the FS in quantum phase transitions (QPTs) is then established on more general grounds. Depending on whether the FS's dimensions of two neighboring quantum phases are the same or not, we are able to classify QPTs into two distinct types. For the latter type, the change in the FS's dimension is a characteristic that separates two phases. As a non-trivial application to the Kitaev honeycomb model, we find that the FS is proportional to L 2 ln L in the gapless phase, while L 2 in the gapped phase. Therefore, the extra dimension of ln L can be used as a characteristic of the gapless phase.

Unsupervised identification of topological phase transitions using predictive models

“…For our particular model, | ( ) b Y ñis given in equation (9). It has been shown, that a divergence or maximum of the fidelity susceptibility χ F indicates a second-order symmetry-breaking quantum phase transition [3][4][5]. Numerical evidence suggests that topological phase transitions are indicated in the same way [6].…”

“…One investigates the derivative of the overlap [2] of two infinitesimally separated ground states | ( ) y b ñ as a function of some tuning parameter β. While this probe is in principle very powerful [3][4][5][6], it is typically hard to evaluate as one has rarely access to the full wave-function. At least not for most of the approximate numerical techniques and especially not in experimental studies.…”

Scaling Behavior of the Ground-State Fidelity in the Lipkin–meshkov–glick Model

“…(13) but with θ given by Eq. (18). A point to note here is that the eigenbasis of a † a is now no longer h-independent since the angle of rotation α in Eq.…”

“…18 For example, χ F ∼ N in the symmetry-broken phase and χ F ∼ N 0 in the polarized phase of the LMG model. 19 Therefore, from Eq.…”

Fidelity and superconductivity in two-dimensionalt−Jmodels

“…The ground-state fidelity, originally studied in the context of quantum information theory, has been shown to be a sensitive indicator of changes in the ground state of manybody systems, as they occur in quantum phase transitions. [26][27][28][29][30][31][32][33][34] The other two observables of interest we will study are the d-wave and extended-s-wave superconductivity condensate occupations. They will be defined carefully in the next section.…”