Scaling dimension of fidelity susceptibility in quantum phase transitions

Details Scaling dimension of fidelity susceptibility in quantum phase transitions Scaling dimension of fidelity susceptibility in quantum phase transitions

2008-07-22

arxiv.org/abs/0807.3491v2

Physics

Quantum Physics

4 pages, 1 figure, final version to appear in EPL

Scientific paper

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.

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