Gunnar Möller's research homepage

Dr Gunnar Möller
Royal Society University Research Fellow
Cavendish Laboratory, University of Cambridge
Theory of Condensed Matter Group

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Welcome to my research pages!

Note: My research group has moved to the Physics of Quantum Materials Group at the School of Physical Sciences , University of Kent, at Canterbury, UK. Information about my activities at Kent can be found here. Applications from potential fellows, postdocs and PhD candidates are welcome. See our webpage for advice on joining the Physics of Quantum Materials Group.

I am always happy to discuss with potential applicants for fellowships.


Guest editor for IOP Journal of Physics: Condensed Matter Special Issue on "Machine Learning in Condensed Matter Physics". Submissions are invited by 30 June 2020 on the call page.

Research interests:

My research on correlated phases of interacting many-body quantum systems is placed at the interface of several active fields of science: cold atomic gases, the fractional quantum Hall effect, frustrated spin systems, and topological quantum computation. Currently, I develop new algorithmic approaches to strongly correlated systems such as heavy-fermion materials and superconductors.

If you are interested in these topics and might like to join my group, please consult the advice listed here.

Some of the highlights of my published research include:

Novel types of correlated phases in cold atomic gases:

The experimental possibilities of manipulating cold atomic gases open up pathways to observe unusual types of order. I have analysed rapidly rotating fermi gases using mean-field theory and a renormalisation group approach to predict a new supersolid phase. My numerical studies of cold atoms on lattices with an effective magnetic field have shown evidence of novel quantum Hall states that differ from those in the continuum.

Topological phases of matter:

Recent proposals for inherently fault tolerant topological quantum computing rely on the existence of two-dimensional phases of matter in which quasiparticles with exotic non-abelian exchange statistics emerge as the low energy excitations. I have a particular interest to understand under which circumstances realistic systems give rise to non-abelian statistics. Specifically, my past work has focused on paired quantum Hall states, developing a description equivalent to BCS trial wavefunctions to enhance the understanding of the nature of the important case of half filled Landau levels. My studies cover possible realizations of non-abelian phases in two dimensional electron gases as well as in cold atomic gases.

Frustrated arrays of nano-magnets:

Frustrated magnetism usually results from incompatible nearest neighbor interactions. I have shown under which circumstances classical two-dimensional spins systems with long range dipolar interactions yield a frustrated magnetic state. My analysis of spins on the kagomé lattice shows that their order is naturally understood in terms of magnetic monopoles as the effective degrees of freedom.

Numerical methods for interacting many-body systems:

Many of my results rely on the use of state-of-the-art simulation techniques for strongly interacting quantum systems. In particular, I use exact diagonalization as a powerful technique in quantum Hall physics and am an active developer of DiagHam, a numerical library for large scale exact diagonalisation calculations. My current developments focus on hybrid approaches uniting numerics and quantum field theory. I also have expertise in a range of Monte Carlo techniques, including variational quantum Monte Carlo, as well as thermodynamic Monte Carlo simulations.


I gratefully acknowledge support from the Royal Society via a University Research Fellowship, now held at the University of Kent. I would like to thank the Theory of Condensed Matter Group and the Cavendish Laboratory for hosting my group prior to my move. I also acknowledge earlier research support by an Early Career Fellowship of the Leverhulme Trust, by a Research Fellowship at Trinity Hall and by a portfolio grant of the EPSRC.


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