Distribution of fidelity zeros in two-band topological models

TL;DR

This paper explores how fidelity zeros in two-band topological models relate to topological phase transitions by analyzing their distribution in complex parameter space, revealing critical points and phase boundaries.

Contribution

It extends the fidelity-zero framework to topological quantum phase transitions, analyzing their distribution in complex parameters for various models.

Findings

Fidelity zeros form discrete lines in finite systems and accumulate in extended regions in the thermodynamic limit.

Critical points of topological transitions are bounded by fidelity zeros crossing the real axis.

The study clarifies how critical information is encoded in the complexified parameter space.

Abstract

We investigate the distribution of fidelity zeros in two-band topological models by extending the phase transition driving parameter into the complex plane. Within the biorthogonal formulation, we unveil that fidelity zeros are related to momentum modes for which the real part of the energy gap vanishes. Guided by this relation, we analyze the Kitaev chain, the Haldane model, and the Qi-Wu-Zhang (QWZ) model. In finite-size systems the zeros form discrete lines parallel to the imaginary axis, while in the thermodynamic limit they accumulate into extended regions in the complex parameter plane. For the Kitaev and Haldane models, the accessible interval of the real part of the complexified parameter is bounded by the critical points of the corresponding topological transitions. For the QWZ model, the transitions at $u = \pm2$ are identified in the same way, whereas the critical point at $u = 0$ is signaled by fidelity zeros crossing the real axis. These results extend the fidelity-zero framework to topological quantum phase transitions and clarify how critical information is encoded in complexified parameter space.