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(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 Areas

Strong correlations and exotic superconductivity in low-dimensional systems

Strongly correlated systems often show the proximity of unconventional superconductivity, non-Fermi liquids and insulating magnetic states of quantum matter. Well known examples include the cuprates and heavy fermion systems. We are interested in understanding how the enhanced quantum fluctuations in low-dimensional (e.g., two dimensional) versions of such systems can enhance the emergence of complexity.


Topological states of matter and symmetry breaking


Topological states of matter are known to be governed by rules that depart from the traditional Ginzburg-Landau-Wilson paradigm of local order parameters and spontaneous symmetry breaking. The entanglement properties of the many-body Hilbert space are believed to be key to the ongoing search for topological order in quantum matter. We are presently focussed on asking how topological order can arise in correlated fermionic quantum matter.

Fermionic quantum criticality
and Lifshitz transitions

Quantum criticality associated with correlated electrons likely require order parameters that describe the geometry and topology of the Fermi surface. We are interested in investigating quantum phase transitions that involve drastic changes in the exchange statistics of excitations lying above the ground state and changes in the topology of the Fermi surface (Lifshitz transitions).


Fustrated magnetism and spin liquids
The study of frustrated magnetism is at the heart of the search for liquid-like states arising in systems of interacting quantum spins. Such states do not display any ordering of the constituent spins even at T=0. Instead, there exist predictions of topological order in some gapped spin liquid states. We are interested in investigating whether such proposals can be realised in geometrically frustrated systems like the Kagome or pyrochlore lattices.
Quantum Materials

Quantum materials are systems that display quantum properties at the macroscale. Various forms of superconductivity and magnetism are well known examples. We are presently exploring the physics of some well known materials (e.g., KCuF3, Mn3O4 etc.) in which the dynamics of orbital and spin degrees of freedom interplay with one another in reaching a variety of ordered ground states. Our goal is to be able to offer predictions towards realising novel emergent states of quantum matter, e.g., the orbital-spin liquid, in a material. 


Quantum Transport

We are interested in studying the interplay of strong correlations, low dimensionality and circuit topology in shaping quantum transport. An example is that of edge transport in an inhomogeneous quantum Hall system.  





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