TY - JOUR
TI - Symplectic-N in strongly correlated materials
DO - https://doi.org/doi:10.7282/T3BP02KJ
PY - 2010
AB - Strong correlations between electrons often generate unexpected new collective behavior that we call emergent phenomena. Strong interactions can ramp up the relevant scales, creating massive electrons in heavy fermion materials and high transition temperatures in superconductors, or lead to entirely new states of matter with low energy excitations containing a fraction of the original electron. These phenomena provide unique challenges to theorists as they sit at the intersection of kinetic and potential energy scales, where perturbative many body techniques fail. One useful method here is the large N approach, which generalizes the number of components of the electron spin from 2 to N, providing an artificial perturbation expansion about a strongly correlated state which, if chosen properly, captures the essential physics. To do so, we must ensure that the large N limit maintains the important symmetries. While SU(N) is the traditional large-N limit, not all SU(N) spins invert under time-reversal for N > 2. To treat phenomena like frustrated magnetism and superconductivity that contain particle-particle singlets, we must restrict ourselves to the subgroup of time-reversing spins, SP(N), a large N limit we call symplectic-N. The correspondance of time-reversal and symplectic symmetry, and its consequences for spin and Hubbard operator representations are discussed in Chapter 2, which provides the mathematical backbone of this dissertation. Chapter 3 develops a symplectic-N treatment of frustrated magnetism, treating ferromagnetic and antiferromagnetic correlations on equal footing, before we move on to unconventional superconductivity. First we show how composite pairs, bound states between local moments and conduction electrons in two orthogonal symmetry channels, emerge from the large N limit of the two channel Kondo model in Chapter 4, and then discuss how composite pairing interacts cooperatively with magnetic pairing in Chapter 5. In Chapter 6, we examine the interplay of composite pairing and valence fluctuations in the two-channel Anderson model. Finally, Chapter 7 studies the effect of Coulomb repulsion on s +/- pairing in a t-J model of the iron-based superconductors.
KW - Physics and Astronomy
KW - Electrons
KW - Superconductivity
KW - Fermions
LA - eng
ER -