are interested in exploring the interplay of low-dimensionality,
strong correlations and quantum fluctuations in leading to novel
emergent states of matter. By
"emergence", we mean that in a many-body system whose
constituents interact with one another, we often find complex
collective behaviour at low energies and long lengthscales that is
qualitatively different from the behaviour of the constituent parts.
Evidence of such emergent complexity can, for instance, be seen in
the phase diagrams of materials like the cuprates, heavy fermion
systems, manganites, pnictides etc. An outstanding feature of such
phase diagrams is the competition (and sometimes even the
coexistence!) of various forms of charge and magnetically ordered
insulating states with superconducting order. Another is the
existence of metallic states which show clear signatures of departure
from Landau’s paradigm for the Fermi liquid. The recent explosion
of interest in topological states of matter beyond the quantum Hall
effects (integer and fractional) offer another fascinating
playground, pointing the way towards strongly correlated forms of
topological insulating and superconducting forms of matter.
theoretical analysis of such phenomena is often challenging due to
the absence of any obvious small coupling constant in the problem.
This is seen from the fact that when the competing tendencies for a
quantum particle to either localise in space (due to inter-particle
correlations, scattering from disorder or lattice vibrations) or to
spread out its wavefunction (due to its kinetic energy) match one
another, any theoretical description typically faces restrictions on
its validity and powers of prediction. In addition, critical
phenomena in low-dimensional systems are often at zero-temperature
and driven by quantum fluctuations arising from the competition
between different quantum orders. Such transitions are called
“quantum phase transitions”, and have been studied widely for
some time now. While such transitions have typically been classified
within the paradigm laid out by Ginzburg, Landau and Wilson, there is
currently great interest in understanding whether emergent complexity
in strongly correlated fermionic quantum matter (e.g., some of the
materials and systems mentioned above) can lie outside this paradigm.
attempting an understanding of the emergent complexity in various
materials, we often adopt a model-based approach. While several
simplifying assumptions are typically made during the analysis, our
aim is to identify the appropriate models and results that offer
universal insight on the phenomena under investigation. We adopt a
variety of analytic methods in this pursuit, including the
development of non-perturbative techniques that can offer enhanced
information on the low-energy quantum dynamics of the many-body
more information, please visit the Research page.
(A) Theory of orbital and
spin ordering phenomena in the Mn3O4 spinel.
(B) Scaling theory for
T=0 ground states of the 2D Hubbard model on the square lattice at. and
away from, half-filling.