A dominant part of my published work is on magnetic systems which is my bread-and-butter topic of research, so to speak. I currently study quantum and classical magnets with competing interactions with a view to characterising their low temperature (which often can be zero temperature, since I am a theorist!) phases. These systems do not usually order, in the layman sense in which we visualise order, but then they are not trivially disordered either. While most practitioners broadly agree that the interplay of correlations and entanglement, the topological nature of the phases and fluctuations (thermal and quantum) all play a role in the formulation of the theory of these phases, there is no agreed upon coherent formalism for many important (and longstanding) problems in the field.
Over the years I have used a variety of different techniques to study some of these systems. I started out in the early days of my career working on one dimensional quantum magnets. I studied frustration induced phase transitions, formation of magnetisation plateaus and the alternation of gapped and gapless phases in several 1d or effectively 1d systems. My last published work in this area involves the study of the effects of competing interactions in a mixed spin ladder using the Density Matrix Renormalisation Group (DMRG). In the last several years I have been working on two and three dimensional spin systems. I have ongoing projects on both classical and quantum magnets which deal with the study of several aspects of frustrated magnets. I study ground state phase diagrams using exact diagonalisation, interplay of exchange and dipolar interactions, aspects of entanglement content, and dynamical correlations at low temperature.
I also spent some time during my days as a student on some aspects of mesoscopic physics. We studied the effects of a magnetic impurity at a junction of Luttinger liquids. Building on existing results for scalar scattering at the junction we evaluated the RG flows of the Kondo couplings assuming weak electronic interactions. I retain interest in that field though I do not have active projects right now.
My work usually requires an equal mix of both analytical and numerical techniques and it is likely to remain that way in the future. I have some interest in computing, which has deepened with time both because it is necessary for my work and also because I quite enjoy writing code. Most of my (computing) time right now is spent on development of parallelised exact diagonalisation based programs. In the past I have also worked with DMRG and Contractor renormalisation techniques among other things.
In the near future I hope to make this page personable with more accessible information. In the meantime please find more details of my research in my publications.