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We 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.

The 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.

In 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 interacting system.

For more information, please visit the Research page.

What's New

(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.

Research Topics

Strong correlations and exotic superconductivity in low-dimensional systems

Fermionic quantum criticality
and Lifshitz transitions

Topological states of matter and symmetry breaking

Frustrated magnetism and spin liquids

Quantum Materials

Quantum Transport

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