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20 lines
1.9 KiB
Markdown
20 lines
1.9 KiB
Markdown
---
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title: "PhD Project"
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subtitle: "The one-dimensional Long-Range Falikov-Kimball Model"
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excerpt: "I study a simplified model of electrons moving about in a crystal."
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collection: portfolio
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image: "phase_diagram.png"
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alt: "A colourful scientific figure from my work."
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---
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## 2018 - 2021 (expected)
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### Plain English
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Building upon the work of others, I study a very simplified model of electrons moving about in a crystal. A crystal is a structure that repeats through space, like the pattern on a chess board. We work in one dimension so in our case it would be more like patterns of coloured beads on a necklace. In addition the crystal is slightly disordered, as if the person making the necklace sometimes gets it a little wrong. This disorder tends to disrupt the movement of the electrons, often meaning that they cannot move at all.
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### Technical English
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Both disorder or interactions can turn metals into insulators. One of the simplest settings to study this physics is given by the Falikov-Kimbal (FK) model describing itinerant fermions interacting with a classical Ising background field. Despite the translational invariance of the model, it has been shown that in-homogenous configurations of the background field give rise to effective disorder physics leading to a rich phase diagram in two (or more) dimensions with finite temperature charge density wave (CDW) transitions and interaction-tuned Anderson versus Mott localized phases. Here, we propose a generalised FK model in one dimension with long-range interactions which shows a similarly rich phase diagram. Using an exact Markov Chain Monte Carlo method we map out the phase diagram and compute the energy resolved localisation properties of the fermions. We compare the behaviour of this transitionally invariant model to an Anderson model of uncorrelated binary disorder about a background CDW field and discuss its experimental implications.
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