Scaling dimension of fidelity susceptibility in quantum phase transitions

TL;DR

This paper investigates the scaling behavior of fidelity susceptibility in quantum phase transitions, revealing that it has a distinct dimension that can classify phases and characterize gapless versus gapped states.

Contribution

It establishes a general scaling relation for fidelity susceptibility and introduces a classification of quantum phase transitions based on the dimension change of FS.

Findings

Fidelity susceptibility has its own dimension, separate from the system's dimension.

The FS scales as L^2 ln L in the gapless phase of the Kitaev model.

The FS scales as L^2 in the gapped phase of the Kitaev model.

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.