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Abstract The search for quantum spin liquids—topological magnets with fractionalized excitations—has been a central theme in condensed matter and materials physics. Despite numerous theoretical proposals, connecting experiment with detailed theory exhibiting a robust quantum spin liquid has remained a central challenge. Here, focusing on the strongly spin-orbit coupled effectiveS = 1/2 pyrochlore magnet Ce₂Zr₂O₇, we analyze recent thermodynamic and neutron-scattering experiments, to identify a microscopic effective Hamiltonian through a combination of finite temperature Lanczos, Monte Carlo, and analytical spin dynamics calculations. Its parameter values suggest the existence of an exotic phase, aπ-flux U(1) quantum spin liquid. Intriguingly, the octupolar nature of the moments makes them less prone to be affected by magnetic disorder, while also hiding some otherwise characteristic signatures from neutrons, making this spin liquid arguably more stable than its more conventional counterparts. 

Abstract The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength (J_eff) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho₂Ti₂O₇, and show that the magneto-chemical potential depends on the spin sublattice (αorβ), i.e., the Pauling state, involved in the transition. Monte Carlo simulations using the dipolar-spin-ice Hamiltonian support our findings of a sublattice-dependent magneto-chemical potential, but the model underestimates theJ_efffor theβ-sublattice. Additional simulations, including next-nearest neighbor interactions (J₂), show that long-range exchange terms in the Hamiltonian are needed to describe the measurements. This demonstrates that torque magnetometry provides a sensitive test forJ_effand the spin-spin interactions that contribute to it. 

High-resolution neutron spectroscopy on ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$reveals a correlated state characterized by distinct dipolar scattering signals—quasielastic and inelastic contributions consistent with ‘photon’ and ‘spinon’ excitations in quantum spin ice. These signals coexist with weak octupolar scattering. Fits of thermodynamic data using numerical methods indicate a dominant octupolar exchange, $J_x$or $J_y$, with substantial dipolar $J_z$and minute dipole-octupole $J_{xz}$couplings. The $J_{xz}$value is corroborated by an independent fit of the neutron scattering amplitude balance between dipolar and octupolar ‘photon’ contributions, highlighting its importance to understand neutron scattering results in this family. ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$enriches the landscape of dipole-octupole pyrochlore physics, and reveals a ‘quantum multipolar liquid’ where hybrid correlations involve multiple terms in the moment series expansion, opening questions regarding their intertwining and hierarchy in quantum phases. 

A central problem in modern condensed matter physics is the understanding of materials with strong electron correlations. Despite extensive work, the essential physics of many of these systems is not understood and there is very little ability to make predictions in this class of materials. In this manuscript we share our personal views on the major open problems in the field of correlated electron systems. We discuss some possible routes to make progress in this rich and fascinating field. This manuscript is the result of the vigorous discussions and deliberations that took place at Johns Hopkins University during a three-day workshop January 27, 28, and 29, 2020 that brought together six senior scientists and 46 more junior scientists. Our hope, is that the topics we have presented will provide inspiration for others working in this field and motivation for the idea that significant progress can be made on very hard problems if we focus our collective energies.