Scaling dimension of fidelity susceptibility in quantum phase transitions

Department of Physics and ITP, The Chinese University of Hong Kong - Hong Kong, China

Corresponding author: sjgu@phy.cuhk.edu.hk

Received: 17 April 2009
Accepted: 15 June 2009

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 L² ln L in the gapless phase, while L² in the gapped phase. Therefore, the extra dimension of ln L can be used as a characteristic of the gapless phase.