【科学综述】​强关联电子的费米动力学对称性：一个全面描述高温超导的模型

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Mike Guidry, Yang Sun, Lian-Ao Wu, and Cheng-Li Wu, Front. Phys. 15(4), 43301 (2020), arXiv: 2003.07994 (65 pages) 

链接：http://journal.hep.com.cn/fop/EN/10.1007/s11467-020-0957-5

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文章回顾了强关联电子的SU(4)模型在铜氧基和铁基超导体中的应用。我们发现通过对BCS理论做自洽推广，即在对关联和强库仑斥力的基础上引入反铁磁，可以系统地解释高温超导的主要特征，而母体化合物的微观细节可以通过参数形式描述。模型系统地提供了一种分离主要和次要物理的机制，表明众多高温超导数据所显示的特征虽然很有趣，但不是解释高温超导机制的核心。我们认为更普遍地，在许多物理领域中观察到的常规和非常规超导和超流体行为的范围之广令人惊讶，是由于产生的等效哈密顿量系统地展现出相似的代数结构，尽管其相应的微观哈密顿量之间可能存在根本性的差异。

Fermion dynamical symmetry and strongly-correlated electrons: A comprehensive model of high-temperature superconductivity

Mike Guidry¹, Yang Sun², Lian-Ao Wu³, Cheng-Li Wu⁴ 

¹Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA

²School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

³IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain, and Department of Theoretical Physics and History of Science, Basque Country University (EHU/UPV), Post Office Box 644, 48080 Bilbao, Spain

⁴Department of Physics, Chung-Yuan Christian University, Chungli, Taiwan 320, China

We review application of the SU(4) model of strongly-correlated electrons to cuprate and iron-based superconductors. A minimal self-consistent generalization of BCS theory to incorporate antiferromagnetism on an equal footing with pairing and strong Coulomb repulsion is found to account systematically for the major features of high-temperature superconductivity, with microscopic details of the parent compounds entering only parametrically. This provides a systematic procedure to separate essential from peripheral, suggesting that many features exhibited by the high-Tc data set are of interest in their own right but are not central to the superconducting mechanism. More generally, we propose that the surprisingly broad range of conventional and unconventional superconducting and superfluid behavior observed across many fields of physics results from the systematic appearance of similar algebraic structures for the emergent effective Hamiltonians, even though the microscopic Hamiltonians of the corresponding parent states may differ radically from each other.

Keywords strongly-correlated electrons, SU(4) model, fermian dynamical symmetry, high-temperature superconductivity

Contents

1 Introduction

  1.1 The adequacy of theoretical tools

  1.2 Areas of some consensus

  1.3 Fundamental issues with little consensus

  1.4 Addressing these issues within a unified framework

2 Truncation of large Hilbert spaces

  2.1 Truncation based on microscopic properties of the weakly-interacting system

  2.2 Emergent-symmetry truncation

  2.3 Spontaneously-broken symmetries

  2.4 Examples of emergent symmetries

3. The dynamical symmetry method

  3.1 Solution algorithm

  3.2 Validity and utility of the approach

4. Strongly-correlated SU(4) electrons

  4.1 Structure of the coherent pair basis

  4.2 The collective operators

  4.3 The SU(4) algebra and subalgebras

  4.4 Collective subspace and associated Hamiltonian

5. The dynamical symmetry limits

  5.1 The SO(4) dynamical-symmetry limit

  5.2 The SU(2) dynamical-symmetry limit

  5.3 The SO(5) dynamical-symmetry limit

6. Generalized SU(4) coherent states

  6.1 Associating coherent states with Lie algebras

  6.2 SU(4) coherent states

  6.3 Generalized quasiparticle transformation

  6.4 Temperature dependence

  6.5 Energy gaps and gap equations

  6.6 Relationship to ordinary BCS and Néel theory

  6.7 Solution of the gap equations at zero temperature

  6.8 Solution of the gap equations for finite temperature

  6.9 Momentum-dependent SU(4) solutions

7. Global implications of SU(4) symmetry

7.1 Physical conditions for closure of the SU(4) algebra

  7.2 Reduction from SO(8) to SU(4) symmetry

  7.3 SU(4) symmetry and an upper doping limit for the superconducting state

  7.4 The antiferromagnetic-superconducting transition

8. Ground-state energy surfaces

  8.1 Energy surfaces in the SO(4) limit

  8.2 Energy surfaces in the SU(2) limit

  8.3 Energy surfaces in the SO(5) limit

  8.4 Critical dynamical symmetries

  8.5 Weakly-broken SO(5) symmetry

9. SU(4) energy gaps

  9.1 Energy-ordering of gaps

  9.2 Generic features of SU(4) gaps

  9.3 The critical doping point

  9.4 Comparison with gap data

  9.5 Competing order and preformed pairs

  9.6 The role of triplet pairs

10. SU(4) phase diagrams

  10.1 The predicted phases

  10.2 Comparison with data

11. Fundamental instabilities

  11.1 Pairing instability with doping

  11.2 Critical dynamical symmetry and inhomogeneity

12.The pseudogap and mean fields13. Anisotropy of the pseudogap

  13.1 Fermi arcs and magnetic quantum oscillations

  13.2 Momentum-dependent SU(4) and the pseudogap

  13.3 Summary: Anisotropy, arcs, and pockets

14. The iron-based superconductors

  14.1 Non-Abelian superconductors

  14.2 Extending SU(4) to iron-based superconductors

  14.3 Unified cuprate and Fe-based superconductivity

15.Relationship with other models

  15.1 SU(4) and BCS models

  15.2 SU(4) and Néel antiferromagnetism

  15.3 SU(4) and Mott insulators

  15.4 SU(4) and resonating valence bond states

  15.5 SU(4) and the Zhang SO(5) model

  15.6 SU(4) and the Hubbard and t-J models

16. High critical temperatures

  16.1 Unification of competing order

  16.2 The generalized Cooper instability and high-Tc

  16.3 An information argument

  16.4 The role of microscopic physics

17. Universality of superconducting and superfluid behavior18. What is special about SU(4) symmetry?

  18.1 The physical meaning of SU(4) symmetry

  18.2 Intuitively correct limits

  18.3 What SU(4) is not

  18.4 Simple descriptions and complex phenomena

19. Summary and conclusions

Appendix A SU(4) subgroups and dynamical symmetries

Acknowledgements

References and notes

个人简介

Mike Guidry is a professor of Department of Physics & Astronomy in University of Tennessee, USA. He is the author of more than 200 journal publications and invited presentations, 3 published textbooks, and 3 textbooks in advanced preparation that address topics in nuclear physics, computational science, advanced educational technology, astronomy, astrophysics, cosmology, general relativity, the mathematics of symmetry in physics, elementary particle physics, relativistic quantum field theory, and condensed matter physics. He has been the lead educational technology developer for a 7 major college textbooks (with multiple editions) in introductory physics, astronomy, biology, genetics, and microbiology, and in projects as diverse as training K-12 teachers to use educational technology effectively and explaining the science behind weapons of mass destruction for emergency first responders. Recently he has developed an online course and conducted workshops in programming modern mobile devices for scientific and educational applications. His primary current research interests lie in development of new algorithms for solving large coupled sets of differential equations in scientific applications, understanding the mechanism for Type Ia supernovae, and developing new many-body techniques for understanding high-temperature superconductors and other strongly-correlated electron systems, and in developing new approaches to quantum Hall physics in graphene. He has won various teaching awards and is responsible for many Web-based and conventional initiatives introducing and explaining science to the public.

孙扬教授，博士生导师，吴有训物理奖获得者。20世纪80年代赴德国留学，1991年获德国慕尼黑工业大学博士学位。曾在西班牙马德里自治大学做博士后，1994起先后在美国Drexel大学，田纳西大学，橡树岭国家实验室，圣母大学工作，并兼任密西根州立大学客座教授。2007年被上海交通大学聘为原子核物理学科带头人，现任上海交通大学物理与天文学院特聘教授、核天体物理中心共同主任，并任中国科学院兰州近代物理所兼职教授及博士生导师、兰州重离子加速器国家实验室学术委员会委员、中国原子能研究院兼职研究员、中科院《科学通报》编委会委员。主要研究方向：长期从事低能原子核物理和多体系统的理论研究，研究方向涉及核结构理论、核天体物理、强关联多体物理以及计算物理等诸多领域。目前感兴趣的研究课题有：原子核多体理论；核同质异能态的性质和应用；非稳定核、超形变核、超重核的结构；高温、高密度、丰质子、丰中子状态下的核结构；天体物理中的核过程；宇宙中的元素合成机制；核物理、粒子物理、和天体物理中的弱相互作用；量子体系的集体运动和相变；高温超导机制、强关联多体系统的理论研究等。主要成果: 参与创立了原子核投影壳模型并在近十年来独立发展了该模型，使该模型在原子核高自旋运动、高K同质异能态、原子核超形变，超重元素结构，核天体物理，弱相互作用等研究领域发挥了重要应用。近年来致力于推动核物理和天体物理的交叉研究，以及凝聚态物理中的多体问题研究。发表过近300篇国际SCI文章，特别是在《Nature》《Nature Physics》《Physical Review Letters》等刊物上发表了许多有影响力的学术文章。与南京大学胡中为先生合著出版《天文学教程》，与杨迎春博士合作出版译著《铀之战-开启核时代的科学博弈》。

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