Quenched randomness strongly affects properties of magnetic materials. Two-dimensional (2D) random singlet (RS) states emerge in the random $J\text{\ensuremath{-}}Q$ model by destroying valence bond solid order with spatial randomness. We examine the 2D RS states in a magnetic field with quantum Monte Carlo simulations. The magnetization and susceptibilities show power-law scaling with magnetic field at low temperature. Moreover, they show one-parameter scaling behavior with $B/T$ , and the scaling functions are remarkably consistent with a phenomenological model of random spin pairs with a singular distribution of interactions. These universal scaling functions can be used to diagnose 2D RS states in experiments.Quenched randomness strongly affects properties of magnetic materials. Two-dimensional (2D) random singlet (RS) states emerge in the random $J\text{\ensuremath{-}}Q$ model by destroying valence bond solid order with spatial randomness. We examine the 2D RS states in a magnetic field with quantum Monte Carlo simulations. The magnetization and susceptibilities show power-law scaling with magnetic field at low temperature. Moreover, they show one-parameter scaling behavior with $B/T$, and the scaling functions are remarkably consistent with a phenomenological model of random spin pairs with a singular distribution of interactions. These universal scaling functions can be used to diagnose 2D RS states in experiments.

arXiv:2312.08919Physical review. B./Physical review. BJan 8, 20253 citations

Random gauge models of the superconductor-insulator transition in two-dimensional disordered superconductors

Enzo Granato

We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass, and a Gaussian phase glass. The first two models describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field, while the last two describe the effects of random negative Josephson-junction couplings or $\ensuremath{\pi}$ junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge- and flux-glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin-film superconductors in a magnetic field, in the large disorder limit.We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass, and a Gaussian phase glass. The first two models describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field, while the last two describe the effects of random negative Josephson-junction couplings or $\ensuremath{\pi}$ junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge- and flux-glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin-film superconductors in a magnetic field, in the large disorder limit.

arXiv:1711.04669Physical review. B./Physical review. BNov 13, 20173 citations

Universality in Quantum Random Magnetic Chains

J. E. Hirsch, Jorge V. José

Springer series in solid-state sciencesJan 1, 19810 citations

Universal conductivity in the boson Hubbard model in a magnetic field

Min-Chul Cha, S. M. Girvin

The universal conductivity at the zero-temperature superconductor-insulator transition of the two-dimensional boson Hubbard model is studied for cases both with and without magnetic field by Monte Carlo simulations of the (2+1)-dimensional classical XY model with disorder represented by random bonds correlated along the imaginary time dimension. The effect of the magnetic field is characterized by the frustration f. From the scaling behavior of the stiffness, we determine the quantum dynamical exponent z, the correlation length exponent \ensuremath{\nu}, and the universal conductivity ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$. For the disorder-free model with f=1/2, we obtain z\ensuremath{\approxeq}1, 1/\ensuremath{\nu}\ensuremath{\approxeq}1.5, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.52\ifmmode\pm\else\textpm\fi{}0.03, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$ is the quantum conductance. We also study the case with f=1/3, in which we find ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.83\ifmmode\pm\else\textpm\fi{}0.06. The value of ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$ is consistent with a theoretical estimate based on the Gaussian model. For the model with random interactions, we find z=1.07\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.27\ifmmode\pm\else\textpm\fi{}0.04 for the case f=0, and z=1.14\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.49\ifmmode\pm\else\textpm\fi{}0.04 for the case f=1/2.The universal conductivity at the zero-temperature superconductor-insulator transition of the two-dimensional boson Hubbard model is studied for cases both with and without magnetic field by Monte Carlo simulations of the (2+1)-dimensional classical XY model with disorder represented by random bonds correlated along the imaginary time dimension. The effect of the magnetic field is characterized by the frustration f. From the scaling behavior of the stiffness, we determine the quantum dynamical exponent z, the correlation length exponent \ensuremath{\nu}, and the universal conductivity ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$. For the disorder-free model with f=1/2, we obtain z\ensuremath{\approxeq}1, 1/\ensuremath{\nu}\ensuremath{\approxeq}1.5, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.52\ifmmode\pm\else\textpm\fi{}0.03, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$ is the quantum conductance. We also study the case with f=1/3, in which we find ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.83\ifmmode\pm\else\textpm\fi{}0.06. The value of ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$ is consistent with a theoretical estimate based on the Gaussian model. For the model with random interactions, we find z=1.07\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.27\ifmmode\pm\else\textpm\fi{}0.04 for the case f=0, and z=1.14\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.49\ifmmode\pm\else\textpm\fi{}0.04 for the case f=1/2.

arXiv:cond-mat/9311022Physical review. B, Condensed matterApr 1, 199458 citations

Universality of boundary magnetizations in one-dimensional magnets

Hitoshi Asakawa, Masuo Suzuki

Physics Letters ASep 1, 19973 citations

B/T

, and the scaling functions are remarkably consistent with a phenomenological model of random spin pairs with a singular distribution of interactions. These universal scaling functions can be used to diagnose 2D RS states in experiments.