ABSTRACT
In this paper we write exactly solvable generalizations of one-dimensional quantum XY and Ising-like models by using 2^{d}-dimensional gamma matrices as the degrees of freedom on each site. We show that these models result in quadratic Fermionic Hamiltonians with Jordan-Wigner-like transformations. We illustrate the techniques using a specific case of four-dimensional gamma matrices and explore the quantum phase transitions present in the model.
ABSTRACT
We study the effect of coupling magnetic impurities to the honeycomb lattice spin-1/2 Kitaev model in its spin-liquid phase. We show that a spin-S impurity coupled to the Kitaev model is associated with an unusual Kondo effect with an intermediate coupling unstable fixed point Kcâ¼J/S separating topologically distinct sectors of the Kitaev model. We also show that the massless spinons in the spin-liquid mediate an interaction of the form Siα2Sjß2/Rij3 between distant impurities unlike the usual dipolar RKKY interaction SiαSjα/Rij3 noted in various 2D impurity problems with a pseudogapped density of states of the spin bath. Furthermore, this long-range interaction is possible only if the impurities (a) couple to more than one neighboring spin on the host lattice and (b) the impurity spin S≠1/2.
ABSTRACT
We study nuclear relaxation in the presence of localized electrons in a two-dimensional electron gas in a disordered delta-doped semiconductor heterostructure and show that this method can reliably probe their magnetic interactions and possible long-range order. In contrast, we argue that transport measurements, the commonly employed tool, may not sometimes distinguish between spatial disorder and long-range order. We illustrate the utility of using the nuclear relaxation method to detect long-range order by analyzing a recent proposal made on the basis of transport measurements, on the spontaneous formation of a two-dimensional Kondo lattice in a 2D electron gas in a heterostructure.
