Abstract:
The study of many-body systems of electrons and spins, where the effects of
Coulomb interactions are not negligible, forms one of the most challenging
open problems in condensed matter physics today. Such “strongly correlated
systems” have traditionally provided a fertile hunting ground for exotic
states of matter, ranging from superconductors to quantum Hall phases.
Amongst these systems are also “frustrated magnets”, systems where the
lattice geometry is crucial in preventing spins from ordering even at very
low temperatures. This leads to exotic "spin liquid" phases, which are
potentially useful for quantum computation and high Tc superconductivity.

The first part of my talk will focus on the multiple challenges that

theorists face today in studying strongly correlated systems and in
detecting the presence of exotic phases. Since there are many competing
states, such as ordered (solid) and liquid phases with similar energy,
advanced numerical methods have been instrumental for progress. In this
spirit I highlight recent successes with techniques such as the density
matrix renormalization group and tensor networks.

The second part of my talk will discuss several aspects of a highly
contentious problem in the field of frustrated magnetism involving the
kagome geometry [1,2], which even after three decades of research still
baffles the community. Several realistic materials, such as
herbertsmithite, possess this geometry, which is why it has seen resurgent
interest in the community. I provide a viewpoint based on our recent
discovery (motivated by a Majumdar-Ghosh type construction) of a previously
missed source or “mother” point [3] in one of the simplest spin models
known in the literature. I explain the existence of several phases that
emerge from this quantum mechanically highly degenerate point and discuss
its impact on the wider phase diagram of the kagome lattice
antiferromagnet. I reconcile several independent findings by providing
evidence that the well studied Heisenberg point is possibly part of a line
of critical points.

[1] H.J. Changlani, A.M. Lauchli, Phys. Rev. B 91, 100407(R) (2015).

[2] K. Kumar, H. J. Changlani, B. Clark, E. Fradkin, Phys. Rev. B 94, 134410 (2016).

[3] H.J. Changlani, D. Kochkov, K. Kumar, B. Clark, E. Fradkin (submitted, 2017).