Fermion dynamical symmetry and strongly-correlated electrons: A comprehensive model of high-temperature superconductivity
Mike Guidry , Yang Sun , Lian-Ao Wu , Cheng-Li Wu
Front. Phys. ›› 2020, Vol. 15 ›› Issue (4) : 43301
Fermion dynamical symmetry and strongly-correlated electrons: A comprehensive model of high-temperature superconductivity
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.
strongly-correlated electrons / SU(4) model / fermian dynamical symmetry / high-temperature superconductivity
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See: |
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For example, see |
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See, for example, |
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For a review, see, Ref. [6] and |
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However the standard methodologies in the elementary particle physics case differ from the ones used here, partially because a relativistic quantum field theory is required there but non-relativistic fields are adequate for the present discussion. An accessible introduction to non- Abelian gauge fields may be found in Gauge Field Theories, An Introduction with Applications, Mike Guidry, Wiley, 1992. |
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The particle–hole symmetry intrinsic to these models does not mean that hole-doped and electron-doped compounds are expected to behave in the same manner. Although the operators and basis states of the model are particle–hole symmetric, the interactions entering the effective Hamiltonian would not be expected to be the same for holedoped and particle-doped compounds. Thus, the physical properties of hole-doped and electron-doped compounds could differ substantially. |
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We employ an isomorphism between the groups SU(4) and SO(6) to label irreducible representations using SO(6) quantum numbers. The representation structure and relationship of SU(4) and SO(6) is discussed in: J. N. Ginocchio, Ann. Phys. 126, 234 (1980) |
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Groups generally may have more than one Casimir invariant. We shall use the term “Casimir”to refer loosely to the lowest-order such invariants (which are generally quadratic in the group generators). In the context of the present discussion, quadratic Casimirs are associated with 2-body interactions at the microscopic level. Higher-order Casimirs are then generally associated with 3-body and higher interactions. The restriction of our Hamiltonians to polynomials of order 2 in the Casimirs is then a physical restriction to consideration of only 1-body and 2-body interactions. |
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Thus the most general SU(4) coherent state depends on eight real variables. The reduction of the coherent state parameters to only two in Eq. (28) follows from requiring time reversal symmetry and assuming conservation of spin projection Szfor the wave function. |
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The competition between dynamical symmetries governing the transition between spherical and deformed nuclei is discussed in §4.5 (in particular, §4.5.4) of Ref. [18]. |
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There also is the U(1) generator of charge density waves in our full U(4)⊃U(1)×SU(4) algebra that does not appear in the Zhang SO(5) algebra. |
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The broken particle number symmetry can be restored by particle-number projection, but in practice this procedure may not be necessary as we are dealing with a system having a very large number of fermions. |
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