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Bartholomew Andrews

Postdoctoral Researcher

University of Zurich

Biography

My name is Bartholomew Andrews (or “Bart” for short) and I am a Postdoctoral Researcher at the University of Zurich working with Titus Neupert and formerly with Alexey Soluyanov († 2019).

I work in the field of condensed matter theory and am interested in modelling and predicting new phases of matter. For this, I develop a wide range of numerical techniques to study exciting physical phenomena, such as topological states, vibrational modes in crystals, and Bose-Einstein condensation.

I carried out my PhD at the University of Cambridge under the supervision of Gunnar Möller and Gareth Conduit, on the “Stability of Topological States and Crystalline Solids". I have also written essays on “Skyrmions” for my MASt at the University of Cambridge, and “Simulating the Expansion of Turbulent Bose-Einstein Condensates” for my MSci at Imperial College London, while visiting Heidelberg University.

My current research, however, is more diverse and not just limited to these fields. Please feel free to get in touch if you would like to connect or collaborate.

Interests

  • Topological Matter
  • Quantum Monte Carlo
  • Crystal Stability
  • Bose-Einstein Condensation

Education

  • PhD in Theoretical Physics, 2019

    University of Cambridge

  • MASt in Applied Mathematics, 2015

    University of Cambridge

  • MSci in Physics with a Year in Europe, 2014

    Imperial College London

Research

I perform research in a wide range of areas, and am always keen to diversify my work. Please contact me if you would like to collaborate.

Topological Matter

Topological phases of matter is an active and rapidly-growing field of research. So far, my focus has been broadly on the fractional quantum Hall effect and the Hofstadter model. During my PhD, I studied a series of lattice-generalised fractional quantum Hall states called fractional Chern insulators. Specifically, we numerically verified a predicted filling fraction series for higher Chern bands in the Hofstadter model using exact diagonalization. Currently, I am investigating fractional quantum Hall states in the flat bands of Moiré superstructures using infinite cylinder density matrix renormalization group. Motivated by the progress in the field of twisted bilayer graphene, we are finding ways to characterize and engineer exotic fractional states in realistic bilayer materials.

  • “Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number |C|>1’', B. Andrews and G. Möller, arXiv:1710.09350 [cond-mat.str-el], Physical Review B, 97 035159 (2018).
  • “Fractional quantum Hall states for Moiré superstructures in the Hofstadter regime’', B. Andrews and A. Soluyanov (in preparation).

Quantum Monte Carlo

Quantum Monte Carlo is a leading numerical technique for electronic structure calculations, and unlike competing techniques, such as density functional theory, can potentially compute energies to arbitrary accuracy. Efficiently computing forces with quantum Monte Carlo however, was a great challenge for the community, mainly due to the heavy tails of the force distribution. After several decades work, forces can now be efficiently computed and are routinely used to relax atoms in molecules and crystals. Using the lessons learned from calculating forces, we implemented a method to compute the matrix of force constants in quantum Monte Carlo. We showed that, for simple molecules, this method can relax atoms more quickly and compute the vibrational eigenfrequencies more accurately, compared to existing algorithms.


Crystal Stability

Much of what we currently understand about crystals today dates back to the Drude theory of solids from 1914. We intuitively think of atoms in a crystal as balls connected by springs, when discussing concepts such as harmonic modes or phonons. However, in this work we show that certain crystals lattices have a zero matrix of force constants and so cannot be thought of with springs. Instead these crystal lattices are stabilized at fourth order. We construct simplified models for crystals in the tight-binding and free-electron limits, and derive a phase diagram for the most energetically favorable crystal lattices in these regimes. Finally, we use this to gain insight into the distribution of crystal structures for elemental solids in the periodic table.

  • “Lattice stability of three-dimensional crystals’', B. Andrews and G. Conduit (under peer review).

Bose-Einstein Condensation

Motivated by recent experiments, I studied numerically the anomalous aspect ratio inversion of ellipsoidal Bose-Einstein condensates once they are released from a harmonic trap. Typically, one would expect that the aspect ratio of a released ellipsoidal condensate would invert due to the larger kinetic energy along the minor axis. The experiments showed, however, that if the condensate contains vortices, or is turbulent, then the aspect ratio stays approximately constant as the cloud expands. For my MSci project, I developed a simulation of this expansion based on solutions of the Gross-Pitaevskii equation, and studied the effect of vortices on aspect ratio inversion.

Software

As part of my research, I spend time developing and maintaining a variety of software repositories.

TeNPy

Tensor Network Python (TeNPy) is an open-source Python repository used for density network normalization group calculations. I am developing this code for my current research, together with Johannes Hauschild and Leon Schoonderwoerd. My main contribution has been the addition of examples for characterizing topological phases from the ground states on an infinite cylinder. For more information, please see the github repo or forum.


CASINO

CASINO is a commercial Fortran repository used for quantum Monte Carlo calculations. Originally designed as an in-house code for the University of Cambridge, CASINO is now used by researchers all over the world. I contributed by adding the capability to directly compute the matrix of force constants in quantum Monte Carlo, together with Yu Yang Liu and Gareth Conduit. For more information, please see our recent paper or the forum.


DiagHam

DiagHam is an open-source C++ repository used for exact diagonalization calculations. I contributed to this code at the start of my PhD and am now developing it further for my current research, together with Gunnar Möller. My main contribution has been the capability to compute density-density correlation functions for the Hofstadter model. For more information, please see the svn repo or wiki.

Notes

To aid science communication and help students, I have compiled a repository of undergraduate teaching resources.

Contact

  • Physik-Institut, Winterthurerstrasse 190, 8057 Zurich, Switzerland
  • Office Y36H70