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My current research concerns the dynamics of condensed matter systems subjected to unusual kinds of disorder. I am working on two substantially different systems:
- Quasicrystals contain periodic features with incommensurate periods: therefore, they cannot be described in terms of Bloch's theorem, and so display several phenomena associated with disorder (e.g. Anderson localisation). However, their behaviour is markedly different from truly disordered systems, too. My work concerns understanding the Anderson localisation transitions in quasicrystals, mostly through 1d and 2d tight-binding models.
- Frustrated magnets are characterised by a thermodynamically large number of equivalent ground states. This complex frustrated vacuum (the spin liquid state) allows for a range of exotic excitations, such as effective magnetic monopoles or a U(1) gauge theory including both electric and (Dirac) magnetic charges.
I analysed the effect of the magnetic monopoles of classical spin ice on the electronic structure of Dy2Ti2O7. Currently, I am working on quantum spin ice, trying to develop a more thorough and intuitive understanding its excitation spectrum, with particular focus on the vison.
In Plain English
My research interest lies in strongly correlated many body systems, that is, large collections of simple “particles” interacting with one another. These interactions are responsible for the behaviour of matter as we know it: a single atom is neither solid nor liquid, none the less, such large-scale physics must arise from atomic properties. The general notion of the whole being more than the sum of its parts is called emergence. Other examples include magnetism, superconductivity and superfluidity.
Often, emergent behaviour can be explained in terms of weakly interacting excitations in the system. These excitations are dubbed quasiparticles because they can be thought of as well-defined, more or less free particles of the strongly interacting system. The nature of quasiparticles is hard to predict: some are quite plain (for example, the quasiparticles describing the interacting electrons in a metal still behave like electrons but with a different mass), some are rather exotic (for example, they can be fractional with, say, 1/3 of an electron's charge).
The systems I focus on are dubbed spin ices: they are collections of atomic spins with a complex pattern of interactions. The quasiparticles of spin ice are magnetic monopoles which are in a sense half a spin: in spin ice, we can cut a magnet bar in half! Further tweaks allow these magnetic monopoles interact with each other in a way resembling normal electromagnetism: electromagnetic radiation, that is, light, is also coming from quasiparticles. My research is about understanding these various quasiparticles and devising experiments which can measure them.
Non-power-law universality in one-dimensional quasicrystals. A. Szabó, U. Schneider, arXiv:1803.09756 (submitted to PRB)
Non-power-law universality in one-dimensional quasicrystals. A. Szabó, U. Schneider
Effects of emergent monopoles on the electronic structure of Dy2Ti2O7. A. Szabó, C. Castelnovo