Fidelity and entanglement entropy for infinite-order phase transitions
Abstract
Here, we study the fidelity and the entanglement entropy for the ground states of quantum systems that have infinite-order quantum phase transitions. In particular, we consider the quantum O(2) model with a spin-S truncation, where there is an infinite-order Gaussian (IOG) transition for S = 1 and there are Berezinskii-Kosterlitz-Thouless (BKT) transitions for S ≥ 2. We show that the height of the peak in the fidelity susceptibility (χF) converges to a finite thermodynamic value as a power law of 1 / L for the IOG transition and as 1 / ln (L) for BKT transitions. The peak position of χF resides inside the gapped phase for both the IOG transition and BKT transitions. On the other hand, the derivative of the block entanglement entropy with respect to the coupling constant $$S^{'}_{vN}$$ has a peak height that diverges as ln2 (L) for S = 1 and ln3 (L) for S ≥ 2 and can be used to locate both kinds of transitions accurately. We include higher-order corrections for finite-size scalings and obtain the value of the central charge consistent with c = 1 predicted by conformal field theory. The crossing point of χF between different system sizes is at the IOG point for S = 1 but is inside the gapped phase for S ≥ 2, while those of $$S^{'}_{vN}$$ are at the phase-transition points for all S truncations. Our work elaborates on how to use the finite-size scaling of χF or $$S^{'}_{vN}$$ to detect infinite-order quantum phase transitions and discusses the efficiency and accuracy of the two methods.
- Publication Date:
- Research Org.:
- Univ. of Iowa, Iowa City, IA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF); National Institutes of Health (NIH)
- OSTI Identifier:
- 1979680
- Grant/Contract Number:
- SC0019139; MRI-1429826; 1S10OD016290-01A1
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 104; Journal Issue: 20; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; materials science; physics; BKT transition; entanglement entropy; phase transitions by order; quantum phase transitions; density matrix renormalization group
Citation Formats
Zhang, Jin. Fidelity and entanglement entropy for infinite-order phase transitions. United States: N. p., 2021.
Web. doi:10.1103/physrevb.104.205112.
Zhang, Jin. Fidelity and entanglement entropy for infinite-order phase transitions. United States. https://doi.org/10.1103/physrevb.104.205112
Zhang, Jin. Thu .
"Fidelity and entanglement entropy for infinite-order phase transitions". United States. https://doi.org/10.1103/physrevb.104.205112. https://www.osti.gov/servlets/purl/1979680.
@article{osti_1979680,
title = {Fidelity and entanglement entropy for infinite-order phase transitions},
author = {Zhang, Jin},
abstractNote = {Here, we study the fidelity and the entanglement entropy for the ground states of quantum systems that have infinite-order quantum phase transitions. In particular, we consider the quantum O(2) model with a spin-S truncation, where there is an infinite-order Gaussian (IOG) transition for S = 1 and there are Berezinskii-Kosterlitz-Thouless (BKT) transitions for S ≥ 2. We show that the height of the peak in the fidelity susceptibility (χF) converges to a finite thermodynamic value as a power law of 1 / L for the IOG transition and as 1 / ln (L) for BKT transitions. The peak position of χF resides inside the gapped phase for both the IOG transition and BKT transitions. On the other hand, the derivative of the block entanglement entropy with respect to the coupling constant $S^{'}_{vN}$ has a peak height that diverges as ln2 (L) for S = 1 and ln3 (L) for S ≥ 2 and can be used to locate both kinds of transitions accurately. We include higher-order corrections for finite-size scalings and obtain the value of the central charge consistent with c = 1 predicted by conformal field theory. The crossing point of χF between different system sizes is at the IOG point for S = 1 but is inside the gapped phase for S ≥ 2, while those of $S^{'}_{vN}$ are at the phase-transition points for all S truncations. Our work elaborates on how to use the finite-size scaling of χF or $S^{'}_{vN}$ to detect infinite-order quantum phase transitions and discusses the efficiency and accuracy of the two methods.},
doi = {10.1103/physrevb.104.205112},
journal = {Physical Review. B},
number = 20,
volume = 104,
place = {United States},
year = {Thu Nov 11 00:00:00 EST 2021},
month = {Thu Nov 11 00:00:00 EST 2021}
}
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