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DR TWISTIT HOW TO
DR TWISTIT SERIES

This work discusses how to think about questions relating to RG and universality in this model, and how to determine whether or not the theory can be realized without fine-tuning (answer: no for the simplest version of the theory, but probably yes for slightly more complicated versions).

RG and stability in the exciton Bose liquid tl dr: The exciton Bose liquid (EBL) is a model of bosons hopping on a square lattice, which is interesting because it exhibits UV / IR mixing: low-energy modes exist on scales all the way down to the lattice spacing.We also give generalized Imry-Ma arguments for the robustness of such multipolar symmetry breaking to disorder. Tl dr: We construct generalized Mermin-Wagner arguments that tell one when thermal and quantum fluctuations prevent multipole symmetries from spontaneously breaking. Spontaneous breaking of multipole symmetries.

DR TWISTIT SERIES

Tl dr: We study a 2+1d lattice field theory which captures a series of transitions between superfluids and topological Mott insulators.

Topological Mott insulators and discontinuous U(1) theta terms.

In particular, the superfluid of the Bose-Hubbard model is replaced by an `Bose-Einstein insulator': a phase which has a BEC and U(1) symmetry breaking, but which is not a superfluid. In this work we study a simple dipole-conserving modification of the Bose-Hubbard model, and show that dipole conservation drastically modifies the phase diagram. Comparatively little attention however has focused on the consequences of dipole conservation for equilibrium physics.

Tl dr: The dynamics of systems with dipole moment conservation has been the subject of intense recent study. This analysis suggests that the spin part of the pairing is a mixture of singlet and triplet, and that the orbital part is either p- or d-wave, with future Andreev tunneling measurements able to distinguish between the two. Tl dr: Experiments have advanced to the point where the pairing symmetry of the superconductor in twisted bilayer graphene can likely be nearly uniquely determined on experimental grounds alone, without relying on any particular assumptions from theory. Pairing symmetry of twisted bilayer graphene: a phenomenological synthesis.Below are links to the papers I've written.