Bose-Glass Phases in Disordered Quantum Magnets

In disordered spin systems with antiferromagnetic Heisenberg exchange, transitions into and out of a magnetic-field-induced ordered phase pass through a unique regime. Using quantum Monte Carlo simulations to study the zero-temperature behavior, these intermediate regions are determined to be a Bose-Glass phase. The localization of field-induced triplons causes a finite compressibility and hence glassiness in the disordered phase.Comment: 4 pages, 4 figure

Magnetic Bose glass phases of coupled antiferromagnetic dimers with site dilution

We numerically investigate the phase diagram of two-dimensional site-diluted coupled dimer systems in an external magnetic field. We show that this phase diagram is characterized by the presence of an extended Bose glass, not accessible to mean-field approximation, and stemming from the localization of two distinct species of bosonic quasiparticles appearing in the ground state. On the one hand, non-magnetic impurities doped into the dimer-singlet phase of a weakly coupled dimer system are known to free up local magnetic moments. The deviations of these local moments from full polarization along the field can be mapped onto a gas of bosonic quasiparticles, which undergo condensation in zero and very weak magnetic fields, corresponding to transverse long-range antiferromagnetic order. An increasing magnetic field lowers the density of such quasiparticles to a critical value at which a quantum phase transition occurs, corresponding to the quasiparticle localization on clusters of local magnets (dimers, trimers, etc.) and to the onset of a Bose glass. Strong finite-size quantum fluctuations hinder further depletion of quasiparticles from such clusters, and thus lead to the appearance of pseudo-plateaus in the magnetization curve of the system. On the other hand, site dilution hinders the field-induced Bose-Einstein condensation of triplet quasiparticles on the intact dimers, and it introduces instead a Bose glass of triplets. A thorough numerical investigation of the phase diagram for a planar system of coupled dimers shows that the two above-mentioned Bose glass phases are continuously connected, and they overlap in a finite region of parameter space, thus featuring a two-species Bose glass. The quantum phase transition from Bose glass to magnetic order in two dimensions is marked by novel universal exponents.Comment: 15 pages, 16 figure

Uncertain Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a nonparametric, data driven method to conduct relative performance measurements among a set of decision making units (DMUs). Efficiency scores are computed based on assessing input and output data for each DMU by means of linear programming. Traditionally, these data are assumed to be known precisely. We instead consider the situation in which data is uncertain, and in this case, we demonstrate that efficiency scores increase monotonically with uncertainty. This enables inefficient DMUs to leverage uncertainty to counter their assessment of being inefficient. Using the framework of robust optimization, we propose an uncertain DEA (uDEA) model for which an optimal solution determines 1) the maximum possible efficiency score of a DMU over all permissible uncertainties, and 2) the minimal amount of uncertainty that is required to achieve this efficiency score. We show that the uDEA model is a proper generalization of traditional DEA and provide a first-order algorithm to solve the uDEA model with ellipsoidal uncertainty sets. Finally, we present a case study applying uDEA to the problem of deciding efficiency of radiotherapy treatments

Adaptive design of nano-scale dielectric structures for photonics

Using adaptive algorithms, the design of nano-scale dielectric structures for photonic applications is explored. Widths of dielectric layers in a linear array are adjusted to match target responses of optical transmission as a function of energy. Two complementary approaches are discussed. The first approach uses adaptive local random updates and progressively adjusts individual dielectric layer widths. The second approach is based on global updating functions in which large subgroups of layers are adjusted simultaneously. Both schemes are applied to obtain specific target responses of the transmission function within selected energy windows, such as discontinuous cut-off or power-law decay filters close to a photonic band edge. These adaptive algorithms are found to be effective tools in the custom design of nano-scale photonic dielectric structures.Comment: 4 pages Revtex, 4 embedded EPS figure

Quantum Phase Transitions in Coupled Dimer Compounds

We study the critical properties in cubic systems of antiferromagnetically coupled spin dimers near magnetic-field induced quantum phase transitions. The quantum critical points in the zero-temperature phase diagrams are determined from quantum Monte Carlo simulations. Furthermore, scaling properties of the uniform magnetization and the staggered transverse magnetization across the quantum phase transition in magnetic fields are calculated. The critical exponents are derived from Ginzburg-Landau theory. We find excellent agreement between the quantum Monte Carlo simulations and the analytical results.Comment: 7 pages, 9 eps-figure

Universal scaling at field-induced magnetic phase transitions

We study field-induced magnetic order in cubic lattices of dimers with antiferromagnetic Heisenberg interactions. The thermal critical exponents at the quantum phase transition from a spin liquid to a magnetically ordered phase are determined from Stochastic Series Expansion Quantum Monte Carlo simulations. These exponents are independent of the interdimer coupling ratios, and converge to the value obtained by considering the transition as a Bose-Einstein condensation of magnons, alpha_(BEC) = 1.5. The scaling results are of direct relevance to the spin-dimer systems TlCuCl_3 and KCuCl_3, and explain the broad range of exponents reported for field-induced ordering transitions.Comment: 4 pages, 4 eps-figure

A Robust Inference Method for Decision-Making in Networks

Social network data collected from digital sources is increasingly being used to gain insights into human behavior. However, while these observable networks constitute an empirical ground truth, the individuals within the network can perceive the network’s structure differently—and they often act on these perceptions. As such, we argue that there is a distinct gap between the data used to model behaviors in a network, and the data internalized by people when they actually engage in behaviors. We find that statistical analyses of observable network structure do not consistently take these discrepancies into account, and this omission may lead to inaccurate inferences about hypothesized network mechanisms. To remedy this issue, we apply techniques of robust optimization to statistical models for social network analysis. Using robust maximum likelihood, we derive an estimation technique that immunizes inference to errors such as false positives and false negatives, without knowing a priori the source or realized magnitude of the error. We demonstrate the efficacy of our methodology on real social network datasets and simulated data. Our contributions extend beyond the social network context, as perception gaps may exist in many other economic contexts