On the theory of spin paramagnetism

Subir Sachdev A

This is a summary of a central argument in recent review articles by the author (Physica A 313 252 (2002), Annals of Physics 303 226 (2003), and Rev. Mod. Phys, July 2003). An effective field theory is derived for the low energy spin singlet excitations in a paramagnetic Mott insulator with collinear spin correlations.

Paul Sophus Epstein

Kanako Yoshizawa, Kazuo Takayanagi

We present the magnetic phase diagram of the $\ensuremath{\nu}=2$ quantum Hall system on the whole $({r}_{s},{E}_{Z})$ plane. We fix the phase boundaries of the paramagnetic and ferromagnetic states by looking for a softening of spin-density excitations in the time-dependent Hartree-Fock theory. A nontrivial phase is obtained in the self-consistent Hartree-Fock theory for ${r}_{s}\ensuremath{\sim}2$ and ${E}_{Z}\ensuremath{\lesssim}0.06\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$, where both the paramagnetic and ferromagnetic states show spin instability. We show that the obtained phase is the spin-density wave (SDW) state, and explain the mechanism how the SDW stabilizes.

Austin Blaquière

Animesh Nanda, Kusum Dhochak, Subhro Bhattacharjee

We study the spin-$1/2$ ferromagnetic Heisenberg-Kitaev-$\mathrm{\ensuremath{\Gamma}}$ model in the anisotropic (Toric code) limit to reveal the nature of the quantum phase transition between the gapped ${Z}_{2}$ quantum spin liquid and a spin-ordered phase (driven by Heisenberg interactions) as well as a trivial paramagnet (driven by pseudodipolar interactions $\mathrm{\ensuremath{\Gamma}}$). The transitions are obtained by a simultaneous condensation of the Ising electric and magnetic charges---the fractionalized excitations of the ${Z}_{2}$ quantum spin liquid. Both these transitions can be continuous and are examples of deconfined quantum critical points. Crucial to our calculations are the symmetry implementations on the soft electric and magnetic modes that become critical. In particular, we find strong constraints on the structure of the critical theory arising from time reversal and lattice translation symmetries with the latter acting as an anyon permutation symmetry that endows the critical theory with a manifestly self-dual structure. We find that the transition between the quantum spin liquid and the spin-ordered phase belongs to a self-dual modified Abelian Higgs field theory while that between the spin liquid and the trivial paramagnet belongs to a self-dual ${Z}_{2}$ gauge theory. We also study the effect of an external Zeeman field to show an interesting similarity between the polarized paramagnet obtained due to the Zeeman field and the trivial paramagnet driven pseudodipolar interactions. Interestingly, both the spin liquid and the spin-ordered phases have easily identifiable counterparts in the isotropic limit and the present calculations may shed insights into the corresponding transitions in the material relevant isotropic limit.

Mirjana Božić, Z. Marić