We propose an experiment to explore the magnetic phase transitions in interacting fermionic Hubbard systems, and describe how to obtain the ferromagnetic phase diagram of itinerant electron systems from these observations. In addition signatures of f
erromagnetic correlations in the observed ground states are found: for large trap radii (trap radius $R_T > 4$, in units of coherence length $xi$), ground states are topological in nature -- a skyrmion in 2D, and a hedgehog in 3D.
We study the quantum paraelectric-ferroelectric transition near a quantum critical point, emphasizing the role of temperature as a finite size effect in time. The influence of temperature near quantum criticality may thus be likened to a temporal Cas
imir effect. The resulting finite-size scaling approach yields $frac{1}{T^2}$ behavior of the paraelectric susceptibility ($chi$) and the scaling form $chi(omega,T) = frac{1}{omega^2} F(frac{omega}{T})$, recovering results previously found by more technical methods. We use a Gaussian theory to illustrate how these temperature-dependences emerge from a microscopic approach; we characterize the classical-quantum crossover in $chi$, and the resulting phase diagram is presented. We also show that coupling to an acoustic phonon at low temperatures ($T$) is relevant and influences the transition line, possibly resulting in a reentrant quantum ferroelectric phase. Observable consequences of our approach for measurements on specific paraelectric materials at low temperatures are discussed.
We analyze the magnetic and electronic properties of the quantum critical heavy fermion superconductor beta-YbAlB4, calculating the Fermi surface and the angular dependence of the extremal orbits relevant to the de Haas--van Alphen measurements. Usin
g a combination of the realistic materials modeling and single-ion crystal field analysis, we are led to propose a layered Kondo lattice model for this system, in which two dimensional boron layers are Kondo coupled via interlayer Yb moments in a $J_{z}=pm 5/2$ state. This model fits the measured single ion magnetic susceptibility and predicts a substantial change in the electronic anisotropy as the system is pressure-tuned through the quantum critical point.
Identifying the time reversal symmetry of spins as a symplectic symmetry, we develop a large N approximation for quantum magnetism that embraces both antiferromagnetism and ferromagnetism. In SU(N), N>2, not all spins invert under time reversal, so w
e have introduced a new large N treatment which builds interactions exclusively out of the symplectic subgroup [SP(N)] of time reversing spins, a more stringent condition than the symplectic symmetry of previous SP(N) large N treatments. As a result, we obtain a mean field theory that incorporates the energy cost of frustrated bonds. When applied to the frustrated square lattice, the ferromagnetic bonds restore the frustration dependence of the critical spin in the Neel phase, and recover the correct frustration dependence of the finite temperature Ising transition.
The recent discovery of two heavy fermion materials PuCoGa_{5} and NpPd_{5}Al_{2} which transform directly from Curie paramagnets into superconductors, reveals a new class of superconductor where local moments quench directly into a superconducting c
ondensate. A powerful tool in the description of heavy fermion metals is the large N expansion, which expands the physics in powers of 1/N about a solvable limit where particles carry a large number (N) of spin components. As it stands, this method is unable to jointly describe the spin quenching and superconductivity which develop in PuCoGa_{5} and NpPd_{5}Al_{2}. Here, we solve this problem with a new class of large N expansion that employs the symplectic symmetry of spin to protect the odd time-reversal parity of spin and sustain Cooper pairs as well-defined singlets. With this method we show that when a lattice of magnetic ions exchange spin with their metallic environment in two distinct symmetry channels, they are able to simultaneously satisfy both channels by forming a condensate of composite pairs between between local moments and electrons. In the tetragonal crystalline environment relevant to PuCoGa_{5} and NpPd_{5}Al_{2} the lattice structure selects a natural pair of spin exchange channels, giving rise to the prediction of a unique anisotropic paired state with g-wave symmetry. This pairing mechanism predicts a large upturn in the NMR relaxation rate above T_{c}, a strong enhancement of Andreev reflection in tunneling measurements and an enhanced superconducting transition temperature T_{c} in Pu doped Np_{1-x}Pu_{x}Pd_{5}Al_{2}.
This online material provides the technical detail for ``Heavy electrons and the symplectic symmetry of spin,(arXiv 0710.1122). Three parts. Part I - symplectic spins, their properties and gauge symmetries. Part II - derivation of two-chanel model fo
r tetragonal heavy electron systems with the view to application to PuCoGa5 and NpPd_5Al_2, symplectic-N mean field theory and computation of NMR relaxation rate. Part III - brief discussion of the application to frustrated magnetism in the J1-J2 model, mainly used to test the method.
The variation in the quasiparticle weight $Z$ on moving around the fermi surface in correlated metals is studied theoretically. Our primary example is a heavy Fermi liquid treated within the standard hybridization mean field theory. The most dramatic
variation in the quasiparticle weight happens in situations where the hybridization vanishes along certain directions in momentum space. Such a hybridization node is demonstrated for a simplified model of a Cerium-based cubic heavy electron metal. We show that the quasiparticle weight varies from almost unity in some directions, to values approaching zero in others. This is accompanied by a similar variation in the quasiparticle effective mass. Some consequences of such hybridization nodes and the associated angle dependence are explored. Comparisons to somewhat similar phenomena in the normal metallic state of the cuprate materials are discussed. A phenomenological picture of the pseudogap state in the cuprates with a large Fermi surface with a severely anisotropic spectral weight is explored.
Physicists have long debated whether the hidden order in URu2Si2 is itinerant or localized, and it remains inaccessible to direct external probes. Recent observation of an overdamped collective mode in this material (C. Weibe et al, Nature Physics 3,
96-100 (2007)), appears to resolve this outstanding issue.
