# Publications by John Chalker

## Magnetism in rare-earth quasicrystals: RKKY interactions and ordering

EPL **110** (2015) ARTN 17002

## Understanding the damage of polymer matrix composites by integrating chemical, morphological and mechanical properties

Proceedings of the American Society for Composites - 30th Technical Conference, ACS 2015 (2015)

Copyright © 2015 by DEStech Publications, Inc. and American Society for Composites. All rights reserved. Detailed physical and mechanical characterization of the matrix as well as the interphases of polymer matrix composites can lead to a more complete understanding of failure mechanisms in polymer matrix composite (PMC). This study illustrates mechanical damage of polymers in both the bulk, as well as around the interphase region through integrated computation & experimentation approach. We have developed a quantum mechanics-molecular dynamics framework, which has enabled the prediction of bond scission under load, creation of intermittent free radicals, and exploration of the potential energy surface for possible secondary reactions immediately following bond scission. In parallel, we have conducted experiments with epoxy systems with varying molecular weight and cross-linker density at different load conditions to benchmark the simulation findings of the chemical species present on fracture surfaces of the polymer. In order to evaluate experimentally molecular level effects of mechanical load in epoxy-systems, detail characterizations were conducted combing spectroscopy (X-ray photoelectron spectroscopy, FT-Infrared spectroscopy), microscopy (HRTEM, AFM-IR, SEM), X-ray diffraction (SAXS) and mechanical testing (3-point bending). Similarly, the nanoscopic nature of interphases of PMCs in terms of topography, chemical mapping/bonding, fractography, and modulus are also studied in order to find a bridge between nanoscopic, microscopic and macroscopic mechanical properties.

## Passive correction of quantum logical errors in a driven, dissipative system: A blueprint for an analog quantum code fabric

PHYSICAL REVIEW A **91** (2015) ARTN 062324

## Doping a topological quantum spin liquid: Slow holes in the Kitaev honeycomb model

PHYSICAL REVIEW B **90** (2014) ARTN 035145

## Phase transitions in three-dimensional loop models and the CPn<sup>-</sup>1 sigma model

Physical Review B - Condensed Matter and Materials Physics **88** (2013)

We consider the statistical mechanics of a class of models involving close-packed loops with fugacity n on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show that the loop models are discretizations of CPn-1 σ models. The finite and infinite loop phases represent, respectively, disordered and ordered phases of the σ model, and we discuss the relationship between loop properties and σ model correlators. On large scales, loops are Brownian in an ordered phase and have a nontrivial fractal dimension at a critical point. We simulate the models, finding continuous transitions between the two phases for n=1,2,3 and first order transitions for n≥4. We also give a renormalization-group treatment of the CPn-1 model that shows how a continuous transition can survive for values of n larger than (but close to) 2, despite the presence of a cubic invariant in the Landau-Ginzburg description. The results we obtain are of broader relevance to a variety of problems, including SU(n) quantum magnets in (2+1) dimensions, Anderson localization in symmetry class C, and the statistics of random curves in three dimensions. © 2013 American Physical Society.

## Solution of a model for the two-channel electronic Mach-Zehnder interferometer

Physical Review B - Condensed Matter and Materials Physics **87** (2013)

We develop the theory of electronic Mach-Zehnder interferometers built from quantum Hall edge states at the Landau level filling factor ν=2, which have been investigated in a series of recent experiments and theoretical studies. We show that a detailed treatment of the dephasing and nonequlibrium transport is made possible by using bosonization combined with refermionization to study a model in which interactions between electrons are short range. In particular, this approach allows a nonperturbative treatment of electron tunneling at the quantum point contacts that act as beam splitters. We find an exact analytic expression at an arbitrary tunneling strength for the differential conductance of an interferometer with arms of equal length and obtain numerically exact results for an interferometer with unequal arms. We compare these results with previous perturbative and approximate ones and with observations. © 2013 American Physical Society.

## Universal statistics of vortex lines.

Phys Rev E Stat Nonlin Soft Matter Phys **85** (2012) 031141-

We study the vortex lines that are a feature of many random or disordered three-dimensional systems. These show universal statistical properties on long length scales, and geometrical phase transitions analogous to percolation transitions but in distinct universality classes. The field theories for these problems have not previously been identified, so that while many numerical studies have been performed, a framework for interpreting the results has been lacking. We provide such a framework with mappings to simple supersymmetric models. Our main focus is on vortices in short-range-correlated complex fields, which show a geometrical phase transition that we argue is described by the CP^{k|k} model (essentially the CP^{n-1} model in the replica limit n→1). This can be seen by mapping a lattice version of the problem to a lattice gauge theory. A related field theory with a noncompact gauge field, the 'NCCP^{k|k} model', is a supersymmetric extension of the standard dual theory for the XY transition, and we show that XY duality gives another way to understand the appearance of field theories of this type. The supersymmetric descriptions yield results relevant, for example, to vortices in the XY model and in superfluids, to optical vortices, and to certain models of cosmic strings. A distinct but related field theory, the RP^{2l|2l} model (or the RP^{n-1} model in the limit n→1) describes the unoriented vortices that occur, for instance, in nematic liquid crystals. Finally, we show that in two dimensions, a lattice gauge theory analogous to that discussed in three dimensions gives a simple way to see the known relation between two-dimensional percolation and the CP^{k|k} σ model with a θ term.

## 3D loop models and the CP(n-1) sigma model.

Phys Rev Lett **107** (2011) 110601-

Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to CP(n-1) sigma models, where n is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for n=1, 2, 3, and first order transitions for n≥5. The results are relevant to line defects in random media, as well as to Anderson localization and (2+1)-dimensional quantum magnets.

## Site dilution in the Kitaev honeycomb model (vol 84, 115146, 2011)

PHYSICAL REVIEW B **84** (2011) ARTN 209901

## Disorder in a quantum spin liquid: flux binding and local moment formation.

Phys Rev Lett **104** (2010) 237203-

We study the consequences of disorder in the Kitaev honeycomb model, considering both site dilution and exchange randomness. We show that a single vacancy binds a flux and induces a local moment. This moment is polarized by an applied field h: in the gapless phase, for small h the local susceptibility diverges as χ(h)∼ln(1/h); for a pair of nearby vacancies on the same sublattice, this even increases to χ(h)∼1/(h[ln(1/h)](3/2)). By contrast, weak exchange randomness does not qualitatively alter the susceptibility but has its signature in the heat capacity, which in the gapless phase is power law in temperature with an exponent dependent on disorder strength.

## Spin freezing in geometrically frustrated antiferromagnets with weak disorder.

Phys Rev Lett **98** (2007) 157201-

We investigate the consequences for geometrically frustrated antiferromagnets of weak disorder in the strength of exchange interactions. Taking as a model the classical Heisenberg antiferromagnet with nearest neighbor exchange on the pyrochlore lattice, we examine low-temperature behavior. We show that spatial modulation of exchange generates long-range effective interactions within the extensively degenerate ground states of the clean system. Using Monte Carlo simulations, we find a spin glass transition at a temperature set by the disorder strength. Disorder of this type, which is generated by random strains in the presence of magnetoelastic coupling, may account for the spin freezing observed in many geometrically frustrated magnets.

## Quantum hall systems, and one-dimensional systems

Proceedings of the 24th Solvay Conference on Physics: Quantum Theory of Condensed Matter (2010) 156-199

After briefly reviewing the main paradigms of our theoretical understanding of the quantum Hall effect, I highlight some issues which I believe are not well understood. Included in those are the robustness of fractional charge at rather high temperature, the elusiveness of the universal limit for the physics of the edge, and the physics of non-abelian quantum Hall states. I conclude with a few comments on the role the physics of the quantum Hall effect plays in some other condensed matter systems.

## Spin dynamics in pyrochlore Heisenberg antiferromagnets.

Phys Rev Lett **102** (2009) 237206-

We study the low temperature dynamics of the classical Heisenberg antiferromagnet with nearest neighbor interaction on the frustrated pyrochlore lattice. We present extensive results for the wave vector and frequency dependence of the dynamical structure factor, obtained from simulations of the precessional dynamics. We also construct a solvable stochastic model for dynamics with conserved magnetization, which accurately reproduces most features of the precessional results. Spin correlations relax at a rate independent of the wave vector and proportional to the temperature.

## SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model.

Phys Rev Lett **101** (2008) 155702-

We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.

## Spin textures and random fields in dirty quantum hall ferromagnets

INT J MOD PHYS B **20** (2006) 2785-2794

Dirty quantum Hall ferromagnets (QHFMs) provide a setting both for new problems in the theory of magnetism with quenched disorder, and for new realisations of old problems. In the first category, the fact that spin textures in Heisenberg QHFMs carry charge leads to a coupling between charged impurities and magnetic order. This coupling drives a zero-temperature transition between a ferromagnet at low disorder and a spin glass at strong disorder, and controls screening and the nature of excitations in the disorder-dominated ground state. In the second category, random fields coupling linearly to the order parameter appear in some Ising QHFMs, and transport measurements appear to indicate field-induced domain states at low temperature.

## Electron Interactions and Transport between Coupled Quantum Hall Edge States

Physical Review Letters **94** (2005) 086804 4pp-

## Disordered quantum Hall ferromagnets and cooperative transport anisotropy

PHYSICA E **22** (2004) 82-85

We discuss the behaviour of a quantum Hall system when two Landau levels with opposite spin and combined filling factor near unity are brought into energetic coincidence using an in-plane component of magnetic field. We focus on the interpretation of recent experiments under these conditions (Phys. Rev. Lett. 86 (2001) 866; Phys. Rev. B 64 (2001) 121305), in which a large resistance anisotropy develops at low temperatures. Modelling the systems involved as Ising quantum Hall ferromagnets, we suggest that this transport anisotropy reflects domain formation induced by a random field arising from isotropic sample surface roughness. (C) 2003 Elsevier B.V. All rights reserved.

## Path integrals, diffusion on SU(2) and the fully frustrated antiferromagnetic spin cluster

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL **37** (2004) PII S0305-4470(04)85036-4

## Network models for chiral symmetry classes of Anderson localisation

ANNALES HENRI POINCARE **4** (2003) S539-S557

## Deconstructing the Liouvillian approach to the quantum Hall plateau transition

PHYSICAL REVIEW B **68** (2003) ARTN 045318