Hypervelocity binary stars: smoking gun of massive binary black holes

The hypervelocity stars recently found in the Galactic halo are expelled from the Galactic center through interactions between binary stars and the central massive black hole or between single stars and a hypothetical massive binary black hole. In this paper, we demonstrate that binary stars can be ejected out of the Galactic center with velocities up to 10^3 km/s, while preserving their integrity, through interactions with a massive binary black hole. Binary stars are unlikely to attain such high velocities via scattering by a single massive black hole or through any other mechanisms. Based on the above theoretical prediction, we propose a search for binary systems among the hypervelocity stars. Discovery of hypervelocity binary stars, even one, is a definitive evidence of the existence of a massive binary black hole in the Galactic center.Comment: 5 pages, 3 figures, shortened version, ApJL in pres

Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets

We study effects of disorder (randomness) in a 2D square-lattice $S=1/2$ quantum spin system, the $J$-$Q$ model with a 6-spin interaction $Q$ supplementing the Heisenberg exchange $J$. In the absence of disorder the system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS) ground states. The VBS breaks $Z_4$ symmetry, and in the presence of arbitrarily weak disorder it forms domains. Using QMC simulations, we demonstrate two kinds of such disordered VBS states. Upon dilution, a removed site leaves a localized spin in the opposite sublattice. These spins form AFM order. For random interactions, we find a different state, with no order but algebraically decaying mean correlations. We identify localized spinons at the nexus of domain walls between different VBS patterns. These spinons form correlated groups with the same number of spinons and antispinons. Within such a group, there is a strong tendency to singlet formation, because of spinon-spinon interactions mediated by the domain walls. Thus, no long-range AFM order forms. We propose that this state is a 2D analog of the well-known 1D random singlet (RS) state, though the dynamic exponent $z$ in 2D is finite. By studying the T-dependent magnetic susceptibility, we find that $z$ varies, from $z=2$ at the AFM--RS phase boundary and larger in the RS phase The RS state discovered here in a system without geometric frustration should correspond to the same fixed point as the RS state recently proposed for frustrated systems, and the ability to study it without Monte Carlo sign problems opens up opportunities for further detailed characterization of its static and dynamic properties. We also discuss experimental evidence of the RS phase in the quasi-two-dimensional square-lattice random-exchange quantum magnets Sr$_2$CuTe$_{1-x}$W$_x$O$_6$.Comment: 31 pages, 29 figures; substantial additions in v2; additional analysis in v

Random-singlet phase in disordered two-dimensional quantum magnets

We study effects of disorder (randomness) in a 2D square-lattice S=1/2 quantum spin system, the J-Q model with a 6-spin interaction Q supplementing the Heisenberg exchange J. In the absence of disorder the system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS) ground states. The VBS breaks Z4 symmetry, and in the presence of arbitrarily weak disorder it forms domains. Using QMC simulations, we demonstrate two kinds of such disordered VBS states. Upon dilution, a removed site leaves a localized spin in the opposite sublattice. These spins form AFM order. For random interactions, we find a different state, with no order but algebraically decaying mean correlations. We identify localized spinons at the nexus of domain walls between different VBS patterns. These spinons form correlated groups with the same number of spinons and antispinons. Within such a group, there is a strong tendency to singlet formation, because of spinon-spinon interactions mediated by the domain walls. Thus, no long-range AFM order forms. We propose that this state is a 2D analog of the well-known 1D random singlet (RS) state, though the dynamic exponent z in 2D is finite. By studying the T-dependent magnetic susceptibility, we find that z varies, from z=2 at the AFM--RS phase boundary and larger in the RS phase The RS state discovered here in a system without geometric frustration should correspond to the same fixed point as the RS state recently proposed for frustrated systems, and the ability to study it without Monte Carlo sign problems opens up opportunities for further detailed characterization of its static and dynamic properties. We also discuss experimental evidence of the RS phase in the quasi-two-dimensional square-lattice random-exchange quantum magnets Sr2CuTe1−xWxO6.Accepted manuscrip

The Educational Achievement of Pupils with Immigrant and Native Mothers: Evidence from Taiwan

This paper takes advantage of the Taiwan Assessment of Student Achievement data set to empirically evaluate whether the test score differentials between pupils with immigrant and native mothers are substantial across subjects, grades and years. Our results show that there exist test score differentials between the two groups after controlling for the students' individual characteristics and family background. The Chinese, Math and English subjects exhibit larger test score gaps relative to Science and Society. We also find that the academic gaps between native students and pupils with mothers from Southeast Asian countries tend to widen, while the students' performance is about the same as that for native students if their mothers are from mainland China, confirming that the language proficiency of immigrant mothers significantly affects pupils' learning. Our empirical results may suggest that remedial teaching (or an equivalent preferential policy) for the lower-grade pupils with immigrant mothers might be required to create a fair environment for learning, and such a policy should take the nationality of those foreign mothers into account