Strong
correlations and exotic superconductivity in low-dimensional systems
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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.
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Topological states of matter and symmetry breaking
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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).
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Fustrated magnetism and spin liquids
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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
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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.
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Quantum Transport
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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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