**Multipolar orders**

The electron, having spin S=1/2, produces a dipolar magnetic field. However, spin and orbital magnetic moments of electrons in solids can conspire to produce higher order moments where the leading contributions to magnetism arise from quadrupole or octupole moments. One place where our group was the first to discover concrete theoretical evidence of octupolar magnetism is in a class of transition metal oxides called "double perovskites", in which two different transition metals occupy the two sublattices of a cubic crystal. In addition to theory work, we have also collaborated with the experimental group of Bruce Gaulin at McMaster University whose experiments first led us down this rabbit hole.

**References**

- “Octupolar order in d-orbital Mott insulators”, A. Paramekanti, D. D. Maharaj, B. D. Gaulin, Physical Review B 101, 054439 (2020)
- "Octupolar vs Neel order in cubic 5d2 double perovskites", D. D. Maharaj, et al, Physical Review Letters 124, 087206 (2020)
- "Multipolar magnetism: Crystal field levels, octupolar order, and orbital loop currents", Sreekar Voleti, et al, Physical Review B 101, 155118 (2020)
- "Octupolar order and Ising criticality", S. Voleti, Arijit Haldar, A. Paramekanti, Physical Review B 104, 174431 (2021)
- "Probing octupolar hidden order via Janus impurities", S. Voleti, et al, npj Quantum Materials 8:42 (2023)

**Quantum spin liquids, Topology and interactions**

The study of quantum magnetism has progressed from examining very simple ordered states such as ferromagnets and antiferromagnets, to valence bond states which feature strong entanglement between pairs of neighboring spins, to more extended types of quantum entanglement. Quantum spin liquids are magnetic states which feature very long-range entanglement and concomitant emergence of unusual excitations such as fractional spin and charge excitations as well as emergent "gauge fields" which one usually encounters in the study of high energy physics. We are examining a variety of such quantum spin liquids uncovering, for example, the first possible example of a 3D quantum spin liquid with a Fermi surface of spinons, and a new mechanism of obtaining chiral spin liquids from melting a tetrahedral spin crystal with noncoplanar spins. More broadly, our work in this area also focuses on the phenomenon of "order by disorder" in frustrated systems, and the interplay of interactions and band topology in driving emergent phases at topological quantum critical points.

**References**

- "Haldane-Hubbard Mott Insulator: Tetrahedral Spin Crystal to Chiral Spin Liquid", C. Hickey, L. Cincio, Z. Papic, A. Paramekanti, arXiv:1509.08461
- “Emergent dome of nematic order around a quantum anomalous Hall critical point”, A. M. Cook, C. Hickey, and A. Paramekanti, Phys. Rev. B 90, 085145 (2014).
- “Gapless Spin Liquids on the 3D Hyper-Kagome Lattice of Na4Ir3O8”, M. Lawler, A. Paramekanti, Y.-B. Kim and L. Balents, Phys. Rev. Lett. 101, 197202 (2008).
- “Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice'': A. Mulder, R. Ganesh, L. Capriotti, and A. Paramekanti, Phys. Rev. B 81, 214419 (2010).

**Ultracold Atomic Gases**

Alkali and alkaline earth atoms cooled to nanoKelvin temperatures become quantum degenerate and can exhibit unusual phases driven by the interplay of Bose or Fermi quantum statistics and atom-atom interactions. We have studied a number of issues for cold atoms moving in optical lattices created by laser light, in which atoms can mimic the phases and dynamics of electrons in solid state crystals. Specifically, we are interested in exploring novel phases created by the effect of synthetic magnetic fields and spin-orbit coupling as well as frustration induced by wavefunctions of higher optical lattice bands, and how one might probe such remarkable states using quench dynamics.

**References**

- “Chiral magnetism and spontaneous spin Hall effect of interacting bosons”, X. Li, S. Natu, A. Paramekanti, and S. Das Sarma, Nature Communications 5:5174 (2014).
- “Formation and detection of a chiral orbital Bose liquid in an optical lattice”, X. Li, A. Paramekanti, A. Hemmerich, W. V. Liu, Nature Communications 5:2305 (2014).
- “Bose Hubbard Models with Synthetic Spin-Orbit Coupling: Mott Insulators, Spin Textures and Superfluidity”, W. S. Cole, S. Zhang, A. Paramekanti, and N. Trivedi, Phys. Rev. Lett. 109, 085302 (2012).
- “Anisotropic quantum quench in the presence of frustration or background gauge fields: A probe of bulk currents and topological chiral edge modes”, M. Killi, S.Trotzky, A. Paramekanti, Phys. Rev. A 86, 063632 (2012).
- “Bose Hubbard Model in a Strong Effective Magnetic Field: Emergence of a Chiral Mott Insulator”, A. Dhar, M. Maji, T. Mishra, R. V. Pai, S. Mukerjee, A. Paramekanti, Phys. Rev.A (Rapid) 85, 041602 (R) (2012).