Probing The Neutrino Sector via A Statistical Approach

We apply the idea of landscape (motivated by string theory) to study the statistical nature of parameters/couplings in the standard model of strong and electroweak interactions. Following the success of this approach on the fermion masses, we discuss the divergent behavior of the probability distributions of other physical parameters/couplings to obtain some insights on the quantities that cannot be measured by current experiments but can be relevant in cosmology, in particular those in the neutrino sector. From a relatively strongly mixed PMNS matrix, we argue that the probability distribution of heavy neutrino mass $P(M)$ does not diverge at $M=0$. This analysis favors the degenerate heavy neutrino scenarios.Comment: 29 pages,7 figure

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