research details

an important class of problems in the interface of statistical physics and condensed matter physics involve investigation of simple models of phases and phase transitions which have their underpinnings— via mappings, extensions, limits or other connections — in condensed matter phenomena. my work primarily lies in this arena.

• phenomena
• models
• methods

phenomena

my work explored(/s) themes of:

• frustrated magnetism and spin liquids
• geometric phase transitions/percolation
• discrete scale invariance
• fractal symmetric phases
• heavy fermions

models

models have a central importance in physics —somewhat more than other quantitative sciences— owing to ideas of ‘universality’. for many questions of interest most microscopic details of a physical system are ‘irrelevant’ — except a few key ingredients like symmetries — which can be captured in minimal toy models.

my research usually involves various such models, among them:

• ising and heisenberg spin models
• dimer and loop models
• hubbard models/ kondo lattice models

methods

the extraordinary richness of behaviour of simple models essentially implies (by theorems of there being no free lunch) that they aren’t easy to solve. computational methods often provide useful, otherwise intractable, insights about such models. my primary workhorses have been monte carlo and renormalisation methods :

• monte carlo methods
  • stochastic series expansion quantum monte carlo (spins/bosons)
  • determinant quantum monte carlo (fermions)
  • various loop and cluster algorithms (classical systems/spins/bosons)
• renormalisation methods
  • tensor network renormalisation
  • monte carlo renormalisation

i have spent time trying to device new cluster algorithms to simulate frustrated systems— generally known to be hard for standard methods. i have also dabbled in basic dmrg and exact diagonalisation methods, and been recently interested in leveraging symbolic computation for my research.