Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
|June 2020||August 2020|
Events for 15 July 2020
Prof. Ben Powell: Spin crossover materials, a playground for many-body physics: antiferroelastic order, spin-state ice, deconfined quasiparticles, and emergent gauge fields
Meeting ID: 286 750 9085
Spin crossover occurs in molecules where two electronic states (high-spin and low-spin) are close enough in energy that one can change the electronic state by temperature, magnetic field, light-irradiation, etc. In crystals such molecules interact via elastic forces and form beautiful patterns of high- and low-spin molecules, known as antiferroelasticity. I will show that a simple model for this, based on balls and springs, can be mapped exactly to an Ising model with long-range interactions. Solving this model allows one to explain which different antiferroelastic orders are observed in which families of materials, and why . On frustrated lattices we predict a new phase of matter: spin-state ice. The low-energy physics of this phase is described by an emergent U(1) gauge field (similar to electromagnetism) and the low-energy excitations carry a fractionalised spin midway between the high-spin and low-spin states (that behave analogously to charged particles) . This is an example of a Coulomb phase. Unlike other Coulomb phases in spin ice, water ice, and some spin liquids, the unique nature of spin crossover compounds gives rise to multiple Coulomb phases in the same material that can be tuned between with temperature alone.
J. Cruddas and B. J. Powell, Structure-property relationships and the mechanisms of multistep transitions in spin crossover materials and frameworks, arXiv:2006.03255
J. Cruddas and B. J. Powell, Spin-state ice in elastically frustrated spin-crossover materials, J. Am. Chem. Soc 141, 19790 (2019).
It has been discovered that the lower bound of Ricci curvature $\kappa$ of a Riemannian manifold can be characterized by the displacement $\kappa$-convexity (in the Optimal transport sense) of the Boltzmann-Shannon entropy. Via this characterization, Sturm (‘06) and Lott-Villani (‘09) defined the well-known notion of “Ricci curvature” for a more general class of metric measure spaces. Inspired by the previous work, Erbar and Maas (‘11) gave the modified definition of this Ricci curvature for discrete Markov chains, and they also described this curvature in terms of Bochner’s inequality and gradient estimate with respect to the heat semigroup (in the spirit of Bakry-\’Emery).
After discussing the history of this entropic Ricci curvature, I will briefly talk about my work on how to apply the gradient estimate to obtain an upper bound of the diameter of the underlying graph of the Markov chains with positive Ricci curvature.
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