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Fermion dynamical symmetry and strongly-correlated electrons

已有 474 次阅读 2020-4-29 09:57 |系统分类:科研笔记


Front. Phys. 15(4), 43301 (2020), arXiv: 2003.07994

65 pages 


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-T 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.





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 fields
13 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-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 behavior
18 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
References and notes

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