### Abstract

Condensed matter systems undergoing second order transition away from the critical fluctuation region are usually described sufficiently well by the mean field approximation. The critical fluctuation region, determined by the Ginzburg criterion, |T/T_{c}−1|≪Gi, is narrow even in high T_{c} superconductors and has universal features well captured by the renormalization group method. However recent experiments on magnetization, conductivity and Nernst effect suggest that fluctuations effects are large in a wider region both above and below T_{c}. In particular some “pseudogap” phenomena and strong renormalization of the mean field critical temperature T_{mf} can be interpreted as strong fluctuations effects that are nonperturbative (cannot be accounted for by “gaussian fluctuations”). The physics in a broader region therefore requires more accurate approach. Self consistent methods are generally “non-conserving” in the sense that the Ward identities are not obeyed. This is especially detrimental in the symmetry broken phase where, for example, Goldstone bosons become massive. Covariant gaussian approximation remedies these problems. The Green's functions obey all the Ward identities and describe the fluctuations much better. The results for the order parameter correlator and magnetic penetration depth of the Ginzburg–Landau model of superconductivity are compared with both Monte Carlo simulations and experiments in high T_{c} cuprates.

Original language | English |
---|---|

Pages (from-to) | 228-254 |

Number of pages | 27 |

Journal | Annals of Physics |

Volume | 380 |

DOIs | |

Publication status | Published - 2017 May 1 |

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### Keywords

- Covariant gaussian approximation
- Ginzburg–Landau
- Magnetic penetration depth
- Superconducting thermal fluctuations
- Ward identity

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*380*, 228-254. https://doi.org/10.1016/j.aop.2017.03.015

**Covariant gaussian approximation in Ginzburg–Landau model.** / Wang, J. F.; Li, D. P.; Kao, H. C.; Rosenstein, B.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 380, pp. 228-254. https://doi.org/10.1016/j.aop.2017.03.015

}

TY - JOUR

T1 - Covariant gaussian approximation in Ginzburg–Landau model

AU - Wang, J. F.

AU - Li, D. P.

AU - Kao, H. C.

AU - Rosenstein, B.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - Condensed matter systems undergoing second order transition away from the critical fluctuation region are usually described sufficiently well by the mean field approximation. The critical fluctuation region, determined by the Ginzburg criterion, |T/Tc−1|≪Gi, is narrow even in high Tc superconductors and has universal features well captured by the renormalization group method. However recent experiments on magnetization, conductivity and Nernst effect suggest that fluctuations effects are large in a wider region both above and below Tc. In particular some “pseudogap” phenomena and strong renormalization of the mean field critical temperature Tmf can be interpreted as strong fluctuations effects that are nonperturbative (cannot be accounted for by “gaussian fluctuations”). The physics in a broader region therefore requires more accurate approach. Self consistent methods are generally “non-conserving” in the sense that the Ward identities are not obeyed. This is especially detrimental in the symmetry broken phase where, for example, Goldstone bosons become massive. Covariant gaussian approximation remedies these problems. The Green's functions obey all the Ward identities and describe the fluctuations much better. The results for the order parameter correlator and magnetic penetration depth of the Ginzburg–Landau model of superconductivity are compared with both Monte Carlo simulations and experiments in high Tc cuprates.

AB - Condensed matter systems undergoing second order transition away from the critical fluctuation region are usually described sufficiently well by the mean field approximation. The critical fluctuation region, determined by the Ginzburg criterion, |T/Tc−1|≪Gi, is narrow even in high Tc superconductors and has universal features well captured by the renormalization group method. However recent experiments on magnetization, conductivity and Nernst effect suggest that fluctuations effects are large in a wider region both above and below Tc. In particular some “pseudogap” phenomena and strong renormalization of the mean field critical temperature Tmf can be interpreted as strong fluctuations effects that are nonperturbative (cannot be accounted for by “gaussian fluctuations”). The physics in a broader region therefore requires more accurate approach. Self consistent methods are generally “non-conserving” in the sense that the Ward identities are not obeyed. This is especially detrimental in the symmetry broken phase where, for example, Goldstone bosons become massive. Covariant gaussian approximation remedies these problems. The Green's functions obey all the Ward identities and describe the fluctuations much better. The results for the order parameter correlator and magnetic penetration depth of the Ginzburg–Landau model of superconductivity are compared with both Monte Carlo simulations and experiments in high Tc cuprates.

KW - Covariant gaussian approximation

KW - Ginzburg–Landau

KW - Magnetic penetration depth

KW - Superconducting thermal fluctuations

KW - Ward identity

UR - http://www.scopus.com/inward/record.url?scp=85017531063&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017531063&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2017.03.015

DO - 10.1016/j.aop.2017.03.015

M3 - Article

AN - SCOPUS:85017531063

VL - 380

SP - 228

EP - 254

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -