Topological Defects on the Lattice I: The Ising model

In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang-Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers-Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.Comment: 45 pages, 9 figure

Truth, context and the reference of statements

The overall project of this MPhil thesis is to defend a version of the view that is often called contextualism in philosophy of language, namely the version of the view that I take Charles Travis to hold. His view is that the meaning a sentence is insufficient for deciding on questions about truth and falsity, and that in arriving at the truth-conditions of an utterance the occasion on which the utterance is made always plays a determining role. In order to defend this view, I focus on a particular sort of example – which I refer to as a ‘Travis case’ – and that Travis uses to support his view. Travis cases, as I present Travis as conceiving of them, are supposed to show that the truth-values of utterances made by using the same sentence can differ, although the meaning of constituent expressions is the same and the sentence is used to speak about the same state of things in the world. I consider two alternative ways of analysing the example, from which Travis’s view does not receive support, and I give arguments as to why these analyses are problematic. By doing this, I aim both to give reasons as to why Travis cases support Travis’s view and to highlight in what respects his view differs from the views that are assumed in the alternative analyses

Thought without Illusion

This thesis targets the part of Gareth Evans’s and John McDowell’s view of singular thought which involves the claim that there can be illusions of thought. Singular thought is, according to Evans and McDowell, an object-dependent thought-content; such thought-content could not be entertained unless the object it is about exists. Nevertheless, in a case of perceptual hallucination, where a subject mistakenly takes it that there is an object in front of him or her, Evans and McDowell think that it can seem to a subject exactly as though he or she is having an object-dependent thought, although the subject is in fact not thinking at all due to the absence of any object to think about. The thesis argues for a rejection of this idea of illusions of object-dependent thought. It is further argued that the idea of illusions of thought can be eliminated from Evans’s and McDowell’s view without abandoning their fundamental insight about how singular thought-content is object-dependent. Following specifically McDowell’s development of the view, it is suggested that singular thought is about the world in virtue of how things cognitively appear to the subject. It is suggested that in an alleged case of illusion of thought, the subject has an object-dependent thought about an object whose existence in part is due to the mind’s directedness in that very episode of singular thinking. Furthermore, Evans’s and McDowell’s respective views of acquaintance are criticised, and an idea about acquaintance as awareness of a wider range of objects than just perceivable objects is put forward. In general, the thesis outlines a revised version of Evans’s and McDowell’s view, a version according to which singular thought, although externalistically individuated, is transparent to the thinker

Thermal fluctuations on the freeze-out surface of heavy-ion collisions and their impact on particle correlations

Particle momentum distributions originating from a quark-gluon plasma asproduced in high-energy nuclear collisions can be influenced by thermalfluctuations in fluid dynamic fields. We study this effect by generalizing thecommonly used kinetic freeze-out prescription by allowing for smallfluctuations around an average in fluid velocity, chemical potentials andtemperature. This leads to the appearance of specific two-body momentumcorrelations. Combining a blast-wave parametrization of the kinetic freeze-outsurface with the thermal correlation functions of an ideal resonance gas, weperform an exploratory study of angular net-charge correlations induced bythermal fluctuations around vanishing chemical potential. We note a diffusionof the near-side peak around $\Delta y=\Delta\phi=0$ induced by variances ofdifferent chemical potentials, which could be investigated experimentally.<br

Study of Genotype X Environment Interaction in Alfalfa Forage Yield

The response of alfalfa (Medicago sativa L.) forage yield to eight Alberta test sites was studied for the 1990 and 1991 production years. Cluster analysis was used to group locations and cultivars. Analyses of variances indicated genotype x environment (location) interaction for the first cut yield, the total yield and the difference between first and second cut yields. The Brooks, Bow Island (irrigation), Bow Island (dryland) and Provost locations always clustered together indicating that three of these four test sites may be eliminated without sacrificing reliability

Measurement Quantum Cellular Automata and Anomalies in Floquet Codes

We investigate the evolution of quantum information under Pauli measurement circuits. We focus on the case of one- and two-dimensional systems, which are relevant to the recently introduced Floquet topological codes. We define local reversibility in context of measurement circuits, which allows us to treat finite depth measurement circuits on a similar footing to finite depth unitary circuits. In contrast to the unitary case, a finite depth locally reversible measurement circuit can implement a translation in one dimension. A locally reversible measurement circuit in two dimensions may also induce a flow of logical information along the boundary. We introduce "measurement quantum cellular automata" which unifies these ideas and define an index in one dimension to characterize the flow of logical operators. We find a $\mathbb{Z}_2$ bulk invariant for two-dimensional Floquet topological codes which indicates an obstruction to having a trivial boundary. We prove that the Hastings-Haah honeycomb code belongs to a class with such obstruction, which means that any boundary must have either nonlocal dynamics, period doubled, or admits anomalous boundary flow of quantum information.Comment: v2 changes: clarified the definition of "locally reversible measurement cycle" (LRMC), and added more examples of boundary circuits for the HH cod

Electrical probes of the non-Abelian spin liquid in Kitaev materials

Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin liquid phase in the Kitaev material $\alpha$-$\mathrm{RuCl}_{3}$. Although the platform is a good Mott insulator, we propose experiments that electrically probe the spin liquid's hallmark chiral Majorana edge state and bulk anyons, including their exotic exchange statistics. We specifically introduce circuits that exploit interfaces between electrically active systems and Kitaev materials to `perfectly' convert electrons from the former into emergent fermions in the latter---thereby enabling variations of transport probes invented for topological superconductors and fractional quantum Hall states. Along the way we resolve puzzles in the literature concerning interacting Majorana fermions, and also develop an anyon-interferometry framework that incorporates nontrivial energy-partitioning effects. Our results illuminate a partial pathway towards topological quantum computation with Kitaev materials.Comment: 35 pages, 17 figure

Electrical Probes of the Non-Abelian Spin Liquid in Kitaev Materials

Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin-liquid phase in the Kitaev material α−RuCl₃. Although the platform is a good Mott insulator, we propose experiments that electrically probe the spin liquid’s hallmark chiral Majorana edge state and bulk anyons, including their exotic exchange statistics. We specifically introduce circuits that exploit interfaces between electrically active systems and Kitaev materials to “perfectly” convert electrons from the former into emergent fermions in the latter—thereby enabling variations of transport probes invented for topological superconductors and fractional quantum-Hall states. Along the way, we resolve puzzles in the literature concerning interacting Majorana fermions, and also develop an anyon-interferometry framework that incorporates nontrivial energy-partitioning effects. Our results illuminate a partial pathway toward topological quantum computation with Kitaev materials

Time-domain anyon interferometry in Kitaev honeycomb spin liquids and beyond

Motivated by recent experiments on the Kitaev honeycomb magnet α-RuCl₃, we introduce time-domain probes of the edge and quasiparticle content of non-Abelian spin liquids. Our scheme exploits ancillary quantum spins that communicate via time-dependent tunneling of energy into and out of the spin liquid's chiral Majorana edge state. We show that the ancillary-spin dynamics reveals the edge-state velocity and, in suitable geometries, detects individual non-Abelian anyons and emergent fermions via a time-domain counterpart of quantum-Hall anyon interferometry. We anticipate applications to a wide variety of topological phases in solid-state and cold-atoms settings