A recent article in Nature describes a new magnetic phase found using quantum Monte Carlo in the Hubbard model on a triangular lattice, where geometric frustration generates kinetic magnetism alongside metallicity. This full quantum calculation exceeds what can be tackled in a Bachelor's Thesis, but the underlying phenomenon — how triangular geometry frustrates spin order — has a classic reference model, the antiferromagnetic Ising model on a triangular lattice, famous because, unlike the square lattice, it does not order at finite temperature (Wannier's result from 1950) and serves as a pedagogical starting point for understanding frustration.
What you gain
The student learns to implement the Metropolis algorithm for the Ising model on different lattice topologies, to measure observables (energy, magnetisation, susceptibility, specific heat, spin correlation function) and to characterise the absence of long-range order through finite-temperature behaviour, comparing it with the unfrustrated case of the square lattice. They can reproduce Wannier's result of residual degeneracy and estimate the residual specific heat, without aiming to reach the quantum regime of the article.
What you need
Statistical physics, quantum mechanics I (to justify the model), computational physics/numerical methods, Python (numpy, scipy, matplotlib); no laboratory equipment required.
Work plan
- Review of the Ising model, Metropolis algorithm, and geometric frustration; implementation on a square lattice as a reference40 h
- Implementation of the model on a triangular lattice with periodic boundary conditions and measurement of thermodynamic observables60 h
- Finite-size study and comparison with Wannier's result (absence of transition, residual entropy)50 h
- Analysis of spin correlations and discussion of the contrast with the quantum kinetic magnetism of the original article30 h
- Writing of the thesis and preparation of the defence40 h
Do not take it if
This is not suitable if the expectation is to reproduce or approach the quantum Hubbard model of the article (which requires quantum Monte Carlo with the sign problem, beyond the scope of a Bachelor's Thesis); nor if the student is looking for an original research result, as the objective here is to rigorously reproduce a well-established classical model.