Dimension of fidelity susceptibility in quantum phases

Shi-Jian Gu

Wing Chi Yu, Ho-Man Kwok, Junpeng Cao +1 more

Taotao Hu, Qi Yang, Kang Xue +4 more

Shi-Jian Gu, Hai-Qing Lin

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.

Gu Shi

Quantum phase transition is one of the most important issues in condensed matter physics,and quantum fidelity is an important concept emerging from quantum information theory.In this paper,we describe as simply as possible the role of fidelity and its leading term,i.e.the so-called fidelity susceptibility,in quantum phase transitions.As a purely geometric quantity,the key advantage of the fidelity approach is that no a priori knowledge of the order parameter is assumed.Specifically,we discuss definitions of the fidelity,the fidelity susceptibility,and the corresponding quantum adiabatic dimension,as well as their role in quantum phase transitions.We also use the Lipkin-Meshkov-Glick model and the Kitaev honeycomb model as examples to clarify these issues.

Silvano Garnerone, Damian F. Abasto, Stephan Haas +1 more

Quantum phase transitions that take place between two distinct topological phases remain an unexplored area for the applicability of the fidelity approach. Here, we apply this method to spin systems in two and three dimensions and show that the fidelity susceptibility can be used to determine the boundary between different topological phases particular to these models, while at the same time offer information about the critical exponent of the correlation length. The success of this approach relies on its independence on local-order parameters or breaking symmetry mechanisms, with which nontopological phases are usually characterized. We also consider a topological insulator-superconducting phase transition in three dimensions and point out the relevant features of fidelity susceptibility at the boundary between these phases.