Two-dimensional Ising models on the honeycomb lattice and the square lattice with striped random impurities are studied to obtain their phase diagrams. Assuming bimodal distributions of the random impurities where all the non-zero couplings have the
same magnitude, exact critical values for the fraction p of ferromagnetic bonds at the zero-temperature (T=0) are obtained. The critical lines in the p-T plane are drawn by numerically evaluating the Lyapunov exponent of random matrix products.
The nature of quantum spin liquids is studied for the spin-$1/2$ antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, $J_1$, and those between next-nearest-neighbor sites, $J_2$. We p
erform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region $0.4< J_2/J_1le 0.6$ sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of $0.4 < J_2/J_1 le 0.5$, while the gapped valence-bond-crystal (VBC) phase is stabilized for $0.5 < J_2/J_1 le 0.6$. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the $C_{4v}$ symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation $langle S(0)S(r)rangle propto 1/r^{z+eta}$ at a long distance $r$ appears to increase from $z+etasim 1$ at $J_2/J_1sim0.4$ toward the continuous transition to the VBC phase at $J_1/J_1sim0.5$. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.
We present the first simultaneous observations of chromospheric anemone jets in solar active regions with Hinode SOT Ca II H broadband filetergram and Ca II K spetroheliogram on the Domeless Solar Telescope (DST) at Hida Observatory. During the coord
inated observation, 9 chromospheric anemone jets were simultaneously observed with the two instruments. These observations revealed three important features, i.e.: (1) the jets are generated in the lower chromosphere, (2) the length and lifetime of the jets are 0.4-5 Mm and 40-320 sec, (3) the apparent velocity of the jets with Hinode SOT are 3-24 km/s, while Ca II K3 component at the jets show blueshifts (in 5 events) in the range of 2- 6 km/s. The chromospheric anemone jets are associated with mixed polarity regions which are either small emerging flux regions or moving magnetic features. It is found that the Ca II K line often show red or blue asymmetry in K2/K1 component: the footpoint of the jets associated with emerging flux regions often show redshift (2-16 km/s), while the one with moving magnetic features show blueshift (around 5 km/s). Detailed analysis of magnetic evolution of the jet foaming regions revealed that the reconnection rate (or canceling rate) of the total magnetic flux at the footpoint of the jets are of order of 10^{16} Mx/s, and the resulting magnetic energy release rate (1.1-10) x 10^{24} erg/s, with the total energy release (1-13) x 10^{26} erg for the duration of the magnetic cancellations, 130s. These are comparable to the estimated total energy, 10^{26} erg, in a single chromospheric anemone jet. An observation-based physical model of the jet is presented. The relation between chromospheric anemone jets and Ellerman bombs is discussed.
A quantum-thermal annealing method using a cluster-flip algorithm is studied in the two-dimensional spin-glass model. The temperature (T) and the transverse field (Gamma) are decreased simultaneously with the same rate along a linear path on the T-Ga
mma plane. We found that the additional pulse of the transverse field to the frozen local spins produces a good approximate solution with a low computational cost.
Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum computation. Th
e present paper reviews the mathematical and theoretical foundation of quantum annealing. In particular, theorems are presented for convergence conditions of quantum annealing to the target optimal state after an infinite-time evolution following the Schroedinger or stochastic (Monte Carlo) dynamics. It is proved that the same asymptotic behavior of the control parameter guarantees convergence both for the Schroedinger dynamics and the stochastic dynamics in spite of the essential difference of these two types of dynamics. Also described are the prescriptions to reduce errors in the final approximate solution obtained after a long but finite dynamical evolution of quantum annealing. It is shown there that we can reduce errors significantly by an ingenious choice of annealing schedule (time dependence of the control parameter) without compromising computational complexity qualitatively. A review is given on the derivation of the convergence condition for classical simulated annealing from the view point of quantum adiabaticity using a classical-quantum mapping.
