Exact zeros of fidelity in finite-size systems as a signature for
probing quantum phase transitions
- URL: http://arxiv.org/abs/2310.11951v1
- Date: Wed, 18 Oct 2023 13:25:14 GMT
- Title: Exact zeros of fidelity in finite-size systems as a signature for
probing quantum phase transitions
- Authors: Yumeng Zeng, Bozhen Zhou, Shu Chen
- Abstract summary: In general, the fidelity $mathcalF(gamma,tildegamma)$ always approaches zero in the thermodynamical limit.
We show that exact zero of fidelity can be always accessed by tuning the magnetic flux.
Our work provides a practicable way to detect quantum phase transition via the calculation of fidelity of finite-size systems.
- Score: 4.889561507168047
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The fidelity is widely used to detect quantum phase transition, which is
characterized by either a sharp change of fidelity or the divergence of
fidelity susceptibility in the thermodynamical limit when the phase-driving
parameter is across the transition point. In this work, we unveil that the
occurrence of exact zero of fidelity in finite-size systems can be applied to
detect quantum phase transitions. In general, the fidelity
$\mathcal{F}(\gamma,\tilde{\gamma})$ always approaches zero in the
thermodynamical limit, due to the Anderson orthogonality catastrophe, no matter
whether the parameters of two ground states ($\gamma$ and $\tilde{\gamma}$) are
in the same phase or different phases, and this makes it difficult to
distinguish whether an exact zero of fidelity exists by finite-size analysis.
To overcome the influence of orthogonality catastrophe, we study finite-size
systems with twist boundary conditions, which can be introduced by applying a
magnetic flux, and demonstrate that exact zero of fidelity can be always
accessed by tuning the magnetic flux when $\gamma$ and $\tilde{\gamma}$ belong
to different phases. On the other hand, no exact zero of fidelity can be
observed if $\gamma$ and $\tilde{\gamma}$ are in the same phase. We demonstrate
the applicability of our theoretical scheme by studying concrete examples,
including the Su-Schrieffer-Heeger model, Creutz model and Haldane model. Our
work provides a practicable way to detect quantum phase transition via the
calculation of fidelity of finite-size systems.
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