Topological Z2Z_2 invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group

A projective symmetry group (PSG) has been regarded as a classification theory of spin liquids. However, it does not include a symmetry-protected topological order of fermionic spinon excitations, and thus the classification of gapped spin liquids is incomplete. We demonstrate the classification beyond PSG by utilizing the Kitaev model on the squareoctagon lattice, where two gapped spin liquids are distinguished by a topological $Z_2$ invariant. This $Z_2$ invariant can be defined solely by the time-reversal and translation symmetries on condition that the time-reversal symmetry is implemented projectively. Thus, it is a hidden class of topological Kitaev spin liquids with helical edge states, which has been ignored for a long time. This suggests that there exists an unknown classification scheme of gapped spin liquids beyond PSG.Comment: 5+2 pages, 3+1 figures, one section is move

Effect of the spin-orbit interaction and the electron phonon coupling on the electronic state in a silicon vacancy

The electronic state around a single vacancy in silicon crystal is investigated by using the Green's function approach. The triply degenerate charge states are found to be widely extended and account for extremely large elastic softening at low temperature as observed in recent ultrasonic experiments. When we include the LS coupling $\lambda_{\rm Si}$ on each Si atom, the 6-fold spin-orbital degeneracy for the $V^{+}$ state with the valence +1 and spin 1/2 splits into $\Gamma_{7}$ doublet groundstates and $\Gamma_{8}$ quartet excited states with a reduced excited energy of $O(\lambda_{\rm Si}/10)$. We also consider the effect of couplings between electrons and Jahn-Teller phonons in the dangling bonds within the second order perturbation and find that the groundstate becomes $\Gamma_{8}$ quartet which is responsible for the magnetic-field suppression of the softening in B-doped silicon.Comment: 4 pages, 2 figure

Hydrogen-Bonded Liquids: Effects of Correlations of Orientational Degrees of Freedom

We improve a lattice model of water introduced by Sastry, Debenedetti, Sciortino, and Stanley to give insight on experimental thermodynamic anomalies in supercooled phase, taking into account the correlations between intra-molecular orientational degrees of freedom. The original Sastry et al. model including energetic, entropic and volumic effect of the orientation-dependent hydrogen bonds (HBs), captures qualitatively the experimental water behavior, but it ignores the geometrical correlation between HBs. Our mean-field calculation shows that adding these correlations gives a more water-like phase diagram than previously shown, with the appearance of a solid phase and first-order liquid-solid and gas-solid phase transitions. Further investigation is necessary to be able to use this model to characterize the thermodynamic properties of the supercooled region.Comment: 7 pages latex, 3 figures EP

Magnetic field-induced one-magnon Raman scattering in the magnon Bose-Einstein condensation phase of TlCuCl3_{3}

We report the observation of the $A_{\rm g}$-symmetric one-magnon Raman peak in the magnon Bose-Einstein condensation phase of TlCuCl$_{3}$. Its Raman shift traces the one-magnon energy at the magnetic $\Gamma$ point, and its intensity is proportional to the squared transverse magnetization. The appearance of the one-magnon Raman scattering originates from the exchange magnon Raman process and reflects the change of the magnetic-state symmetry. Using the bond-operator representation, we theoretically clarify the Raman selection rules, being consistent with the experimental results.Comment: 6 pages, 4 figure

Emergence of noncollinear magnetic ordering in small magnetic clusters: Mnn_n and As@Mnn_n

Using first-principles density functional calculations, we have studied the magnetic ordering in pure Mn$_n$ ($n=2-$10, 13, 15, 19) and As@Mn$_n$ ($n=1-$10) clusters. Although, for both pure and doped manganese clusters, there exists many collinear and noncollinear isomers close in energy, the smaller clusters with $n\leqslant$5 have collinear magnetic ground state and the emergence of noncollinear ground states is seen for $n\geqslant$6 clusters. Due to strong $p-d$ hybridization in As@Mn$_n$ clusters, the binding energy is substantially enhanced and the magnetic moment is reduced compared to the corresponding pure Mn$_n$ clusters.Comment: 10 Pages and 5 Figure

CFL Phase of High Density QCD at Non Zero Strange Quark Mass

We compute free energy of quark matter at asymptotically high baryon number density in the presence of non zero strange quark mass including dynamics of pseudo Nambu-Goldstone bosons due to chiral symmetry breaking, extending previously existing analysis based on perturbative expansion in $m_s^2/4\mu\Delta.$ We demonstrate that the CFL$K^0$ state has lower free energy than the symmetric CFL state for $0<m_s^2/4\mu\Delta<2/3$. We also calculate the spectrum of the fermionic quasiparticle excitations about the kaon condensed ground state in the regime $m_s^2/4\mu\Delta \sim 1$ and find that $(m_s^2/4\mu\Delta)_{crit}=2/3$ for the CFL-gCFL phase transition, the leading order result reported in [1], is not modified.Comment: 16 pages, 3 figure